Praying the Rosary
In the beginning of his 2002 encyclical on the Rosary, Pope John Paul II said:
The Rosary, though clearly Marian in character, is at heart a Christocentric prayer. In the sobriety of its elements, it has all the depth of the Gospel message in its entirety, of which it can be said to be a compendium. It is an echo of the prayer of Mary, her perennial Magnificat for the work of the redemptive Incarnation which began in her virginal womb. With the Rosary, the Christian people sits at the school of Mary and is led to contemplate the beauty on the face of Christ and to experience the depths of his love. Through the Rosary the faithful receive abundant grace, as though from the very hands of the Mother of the Redeemer. 
Reflecting on parts of that encyclical will help us pray it with greater devotion and meaning. The whole letter is worth reading, for its rich recounting of the history and past reflections on the Rosary by the Church, but we highlight here the changes which the Holy Father suggested for praying the Rosary - those which are widely known and those which have not been publicized very widely.
The first change which the Holy Father makes in the tradition of reciting the Rosary is the one which received the most publicity.
A proposed addition to the traditional pattern
The Holy Father reflects on the mysteries in the Rosary and add the "Mysteries of Light," explaining their importance.
Of the many mysteries of Christ's life, only a few are indicated by the Rosary in the form that has become generally established with the seal of the Church's approval. The selection was determined by the origin of the prayer, which was based on the number 150, the number of the Psalms in the Psalter.
I believe, however, that to bring out fully the Christological depth of the Rosary it would be suitable to make an addition to the traditional pattern which, while left to the freedom of individuals and communities, could broaden it to include the mysteries of Christ's public ministry between his Baptism and his Passion. In the course of those mysteries we contemplate important aspects of the person of Christ as the definitive revelation of God. Declared the beloved Son of the Father at the Baptism in the Jordan, Christ is the one who announces the coming of the Kingdom, bears witness to it in his works and proclaims its demands. It is during the years of his public ministry that the mystery of Christ is most evidently a mystery of light: “While I am in the world, I am the light of the world” (Jn 9:5).
Consequently, for the Rosary to become more fully a “compendium of the Gospel”, it is fitting to add, following reflection on the Incarnation and the hidden life of Christ (the joyful mysteries) and before focusing on the sufferings of his Passion (the sorrowful mysteries) and the triumph of his Resurrection (the glorious mysteries), a meditation on certain particularly significant moments in his public ministry (the mysteries of light). This addition of these new mysteries, without prejudice to any essential aspect of the prayer's traditional format, is meant to give it fresh life and to enkindle renewed interest in the Rosary's place within Christian spirituality as a true doorway to the depths of the Heart of Christ, ocean of joy and of light, of suffering and of glory. 
Then, the Holy Father comments further on each of the familiar mysteries. What he says about the Mysteries of Light is worth repeating here, in full.
The Mysteries of Light
Moving on from the infancy and the hidden life in Nazareth to the public life of Jesus, our contemplation brings us to those mysteries which may be called in a special way “mysteries of light”. Certainly the whole mystery of Christ is a mystery of light. He is the “light of the world” (Jn 8:12). Yet this truth emerges in a special way during the years of his public life, when he proclaims the Gospel of the Kingdom. In proposing to the Christian community five significant moments – “luminous” mysteries – during this phase of Christ's life, I think that the following can be fittingly singled out: (1) his Baptism in the Jordan, (2) his self-manifestation at the wedding of Cana, (3) his proclamation of the Kingdom of God, with his call to conversion, (4) his Transfiguration, and finally, (5) his institution of the Eucharist, as the sacramental expression of the Paschal Mystery.
Each of these mysteries is a revelation of the Kingdom now present in the very person of Jesus. The Baptism in the Jordan is first of all a mystery of light. Here, as Christ descends into the waters, the innocent one who became “sin” for our sake (cf. 2Cor 5:21), the heavens open wide and the voice of the Father declares him the beloved Son (cf. Mt 3:17 and parallels), while the Spirit descends on him to invest him with the mission which he is to carry out. Another mystery of light is the first of the signs, given at Cana (cf. Jn 2:1- 12), when Christ changes water into wine and opens the hearts of the disciples to faith, thanks to the intervention of Mary, the first among believers. Another mystery of light is the preaching by which Jesus proclaims the coming of the Kingdom of God, calls to conversion (cf. Mk 1:15) and forgives the sins of all who draw near to him in humble trust (cf. Mk 2:3-13; Lk 7:47- 48): the inauguration of that ministry of mercy which he continues to exercise until the end of the world, particularly through the Sacrament of Reconciliation which he has entrusted to his Church (cf. Jn 20:22-23). The mystery of light par excellence is the Transfiguration, traditionally believed to have taken place on Mount Tabor. The glory of the Godhead shines forth from the face of Christ as the Father commands the astonished Apostles to “listen to him” (cf. Lk 9:35 and parallels) and to prepare to experience with him the agony of the Passion, so as to come with him to the joy of the Resurrection and a life transfigured by the Holy Spirit. A final mystery of light is the institution of the Eucharist, in which Christ offers his body and blood as food under the signs of bread and wine, and testifies “to the end” his love for humanity (Jn 13:1), for whose salvation he will offer himself in sacrifice.
In these mysteries, apart from the miracle at Cana, the presence of Mary remains in the background. The Gospels make only the briefest reference to her occasional presence at one moment or other during the preaching of Jesus (cf. Mk 3:31-5; Jn 2:12), and they give no indication that she was present at the Last Supper and the institution of the Eucharist. Yet the role she assumed at Cana in some way accompanies Christ throughout his ministry. The revelation made directly by the Father at the Baptism in the Jordan and echoed by John the Baptist is placed upon Mary's lips at Cana, and it becomes the great maternal counsel which Mary addresses to the Church of every age: “Do whatever he tells you” (Jn 2:5). This counsel is a fitting introduction to the words and signs of Christ's public ministry and it forms the Marian foundation of all the “mysteries of light”. 
The rest of the Holy Father's reflections on the Rosary and his other suggestions for improving our praying the Rosary did not get media attention. They are worth more serious attention.
In many beautiful ways, he re-emphasizes and explains the importance of the Rosary as a method of contemplation, as a preface to his main suggestions. He affirms that the Rosary is "a valid method of prayer," which he says, "can nevertheless be improved."
In effect, the Rosary is simply a method of contemplation. As a method, it serves as a means to an end and cannot become an end in itself. All the same, as the fruit of centuries of experience, this method should not be undervalued. In its favour one could cite the experience of countless Saints. This is not to say, however, that the method cannot be improved. Such is the intent of the addition of the new series of mysteria lucis [mysteries of light] to the overall cycle of mysteries and of the few suggestions which I am proposing in this Letter regarding its manner of recitation. These suggestions, while respecting the well-established structure of this prayer, are intended to help the faithful to understand it in the richness of its symbolism and in harmony with the demands of daily life. Otherwise there is a risk that the Rosary would not only fail to produce the intended spiritual effects, but even that the beads, with which it is usually said, could come to be regarded as some kind of amulet or magic object, thereby radically distorting their meaning and function. 
Announcing each mystery
The Holy Father encourages us to reflect on each mystery deeply, even imaginatively, with a contemplative prayer, he suggests, like St. Ignatius proposed in the Spiritual Exercises. See our site on using the imagination this way.
Listening to the word of God
The Holy Father suggests we read the scripture passage we will reflect upon in each mystery.
It is helpful to follow the announcement of the mystery with the proclamation of a related Biblical passage, long or short, depending on the circumstances. No other words can ever match the efficacy of the inspired word. As we listen, we are certain that this is the word of God, spoken for today and spoken “for me”.
If received in this way, the word of God can become part of the Rosary's methodology of repetition without giving rise to the ennui derived from the simple recollection of something already well known. It is not a matter of recalling information but of allowing God to speak. In certain solemn communal celebrations, this word can be appropriately illustrated by a brief commentary. 
Then the Holy Father recommends something we often forget about in our prayer - reflective silence.
Listening and meditation are nourished by silence. After the announcement of the mystery and the proclamation of the word, it is fitting to pause and focus one's attention for a suitable period of time on the mystery concerned, before moving into vocal prayer. A discovery of the importance of silence is one of the secrets of practicing contemplation and meditation. One drawback of a society dominated by technology and the mass media is the fact that silence becomes increasingly difficult to achieve. Just as moments of silence are recommended in the Liturgy, so too in the recitation of the Rosary it is fitting to pause briefly after listening to the word of God, while the mind focuses on the content of a particular mystery. 
The “Our Father”
Now the Holy Father places the Lord's Prayer in its context for the reflection on the mysteries.
After listening to the word and focusing on the mystery, it is natural for the mind to be lifted up towards the Father. In each of his mysteries, Jesus always leads us to the Father, for as he rests in the Father's bosom (cf. Jn 1:18) he is continually turned towards him. He wants us to share in his intimacy with the Father, so that we can say with him: “Abba, Father” (Rom 8:15; Gal 4:6). By virtue of his relationship to the Father he makes us brothers and sisters of himself and of one another, communicating to us the Spirit which is both his and the Father's. Acting as a kind of foundation for the Christological and Marian meditation which unfolds in the repetition of the Hail Mary, the Our Father makes meditation upon the mystery, even when carried out in solitude, an ecclesial experience. 
The ten “Hail Marys”
Here the Holy Father writes eloquently about the meaning of the repetition of the Hail Mary prayer, as we meditate on each mystery.
This is the most substantial element in the Rosary and also the one which makes it a Marian prayer par excellence. Yet when the Hail Mary is properly understood, we come to see clearly that its Marian character is not opposed to its Christological character, but that it actually emphasizes and increases it. The first part of the Hail Mary, drawn from the words spoken to Mary by the Angel Gabriel and by Saint Elizabeth, is a contemplation in adoration of the mystery accomplished in the Virgin of Nazareth. These words express, so to speak, the wonder of heaven and earth; they could be said to give us a glimpse of God's own wonderment as he contemplates his “masterpiece” – the Incarnation of the Son in the womb of the Virgin Mary. If we recall how, in the Book of Genesis, God “saw all that he had made” (Gen 1:31), we can find here an echo of that “pathos with which God, at the dawn of creation, looked upon the work of his hands”. The repetition of the Hail Mary in the Rosary gives us a share in God's own wonder and pleasure: in jubilant amazement we acknowledge the greatest miracle of history. Mary's prophecy here finds its fulfilment: “Henceforth all generations will call me blessed” (Lk 1:48). 
He then calls our attention to a custom which Pope Paul VI recommended - adding the name of the mystery into the Hail Mary prayer, after the name of Jesus. For example, " and blessed is the fruit of thy womb, Jesus, as we meditate on the mystery of the visitation of Mary to Elizabeth."
The centre of gravity in the Hail Mary, the hinge as it were which joins its two parts, is the name of Jesus. Sometimes, in hurried recitation, this centre of gravity can be overlooked, and with it the connection to the mystery of Christ being contemplated. Yet it is precisely the emphasis given to the name of Jesus and to his mystery that is the sign of a meaningful and fruitful recitation of the Rosary. Pope Paul VI drew attention, in his Apostolic Exhortation Marialis Cultus, to the custom in certain regions of highlighting the name of Christ by the addition of a clause referring to the mystery being contemplated. This is a praiseworthy custom, especially during public recitation. It gives forceful expression to our faith in Christ, directed to the different moments of the Redeemer's life. It is at once a profession of faith and an aid in concentrating our meditation, since it facilitates the process of assimilation to the mystery of Christ inherent in the repetition of the Hail Mary. When we repeat the name of Jesus – the only name given to us by which we may hope for salvation (cf. Acts 4:12) – in close association with the name of his Blessed Mother, almost as if it were done at her suggestion, we set out on a path of assimilation meant to help us enter more deeply into the life of Christ. 
The Holy Father writes about the importance of the prayer, "Glory be to the Father and to the Son and to the Holy Spirit" between each mystery.
Trinitarian doxology is the goal of all Christian contemplation. For Christ is the way that leads us to the Father in the Spirit. If we travel this way to the end, we repeatedly encounter the mystery of the three divine Persons, to whom all praise, worship and thanksgiving are due. It is important that the Gloria, the high-point of contemplation, be given due prominence in the Rosary. In public recitation it could be sung, as a way of giving proper emphasis to the essentially Trinitarian structure of all Christian prayer.
To the extent that meditation on the mystery is attentive and profound, and to the extent that it is enlivened – from one Hail Mary to another – by love for Christ and for Mary, the glorification of the Trinity at the end of each decade, far from being a perfunctory conclusion, takes on its proper contemplative tone, raising the mind as it were to the heights of heaven and enabling us in some way to relive the experience of Tabor, a foretaste of the contemplation yet to come: “It is good for us to be here!” (Lk 9:33). 
Then the Holy Father makes his most dramatic suggestion, which received no mention in the media. Without diminishing the value of current prayers between the mysteries - like the prayer, "Oh, My Jesus, forgive us our sins ..." he suggests replacing those with a Collect - a concluding prayer at the end of each decade's reflection, with "a prayer for the fruits specific to that particular mystery."
The concluding short prayer
In current practice, the Trinitarian doxology is followed by a brief concluding prayer which varies according to local custom. Without in any way diminishing the value of such invocations, it is worthwhile to note that the contemplation of the mysteries could better express their full spiritual fruitfulness if an effort were made to conclude each mystery with a prayer for the fruits specific to that particular mystery. In this way the Rosary would better express its connection with the Christian life. One fine liturgical prayer suggests as much, inviting us to pray that, by meditation on the mysteries of the Rosary, we may come to “imitate what they contain and obtain what they promise”.
Such a final prayer could take on a legitimate variety of forms, as indeed it already does. In this way the Rosary can be better adapted to different spiritual traditions and different Christian communities. It is to be hoped, then, that appropriate formulas will be widely circulated, after due pastoral discernment and possibly after experimental use in centres and shrines particularly devoted to the Rosary, so that the People of God may benefit from an abundance of authentic spiritual riches and find nourishment for their personal contemplation. 
We can experiment, as he suggests, with various spontaneous prayers. For example, at the end of the decade reflecting on on the Annunciation, we might conclude:
"Lord, we thank you for this reflection on the mystery of your Incarnation which happened through the announcement to Mary, your mother. Please give me/us her ready and complete trust in your ways and her acceptance of your call to be your servant in fulfilling your love for others. We ask this in Jesus' name."
As the Holy Father suggests, this kind of prayer helps us focus the reflection on a grace, a fruit we are looking for, as we pray about this mystery. It will be a tremendous grace for us to even ask ourselves, "As I pray this mystery, what is the fruit that it might bring me?"
The plan for using the various mysteries has been publicized broadly - what days we reflect upon which mystery. The Holy Father outlines it here and explains how Thursday and Saturday become days for praying the mysteries of light:
According to current practice, Monday and Thursday are dedicated to the “joyful mysteries”, Tuesday and Friday to the “sorrowful mysteries”, and Wednesday, Saturday and Sunday to the “glorious mysteries”. Where might the “mysteries of light” be inserted? If we consider that the “glorious mysteries” are said on both Saturday and Sunday, and that Saturday has always had a special Marian flavour, the second weekly meditation on the “joyful mysteries”, mysteries in which Mary's presence is especially pronounced, could be moved to Saturday. Thursday would then be free for meditating on the “mysteries of light”. 
In the conclusion of the encyclical, the Holy Father entrusts the power of the Rosary's prayer to the cause of peace and to the cause of the family. [39-42]
He says, "Dear brothers and sisters! A prayer so easy and yet so rich truly deserves to be rediscovered by the Christian community."  And, after appealing to Bishops, priest, deacons and religious to take up the Rosary and to promote it, he says to all of us:
I look to all of you, brothers and sisters of every state of life, to you, Christian families, to you, the sick and elderly, and to you, young people: confidently take up the Rosary once again. Rediscover the Rosary in the light of Scripture, in harmony with the Liturgy, and in the context of your daily lives.