The Rosary is a Scripture-based prayer. It begins with the Apostles' Creed, which summarizes the great mysteries of the Catholic faith. The Our Father, which introduces each mystery, is from the Gospels. The first part of the Hail Mary is the angel's words announcing Christ's birth and Elizabeth's greeting to Mary. St. Pius V officially added the second part of the Hail Mary. The Mysteries of the Rosary center on the events of Christ's life. There are four sets of Mysteries: Joyful, Sorrowful, Glorious and––added by Pope John Paul II in 2002––the Luminous.

The repetition in the Rosary is meant to lead one into restful and contemplative prayer related to each Mystery. The gentle repetition of the words helps us to enter into the silence of our hearts, where Christ's spirit dwells. The Rosary can be said privately or with a group.

The Five Joyful Mysteries are traditionally prayed on the Mondays, Saturdays, and Sundays of Advent:

1. The Annunciation
2. The Visitation
3. The Nativity
4. The Presentation in the Temple
5. The Finding in the Temple

The Five Sorrowful Mysteries are traditionally prayed on the Tuesday, Friday, and Sundays of Lent:

1. The Agony in the Garden
2. The Scourging at the Pillar
3. The Crowning with Thorns
4. The Carrying of the Cross
5. The Crucifixion and Death

The  Five Glorious Mysteries are traditionally prayed on the Wednesday and Sundays outside of Lent and Advent:

1. The Resurrection
2. The Ascension
3. The Descent of the Holy Spirit
4. The Assumption
5. The Coronation of Mary

The Five Luminous Mysteries are traditionally prayed on Thursdays:

1. The Baptism of Christ in the Jordan
2. The Wedding Feast at Cana
3. Jesus' Proclamation of the Coming of the Kingdom of God
4. The Transfiguration
5. The Institution of the Eucharist

Praying the Rosary

Familiarize yourself and/or your group with the prayers of the rosary.

1. Make the Sign of the Cross.
2. Holding the Crucifix, say the Apostles' Creed.
3. On the first bead, say anOur Father.
4. Say three Hail Marys on each of the next three beads.
5. Say the Glory Be
6. For each of the five decades, announce the Mystery (perhaps followed by a brief reading from Scripture) then say the Our Father.
7. While fingering each of the ten beads of the decade, next say ten Hail Marys while meditating on the Mystery. Then say a Glory Be.
   (After finishing each decade, some say the following prayer requested by the Blessed Virgin Mary at Fatima: O my Jesus, forgive us our sins, save us from the fires of hell; lead all souls to Heaven, especially those who have most need of your mercy.)
8. After saying the five decades, say the "Hail, Holy Queen, followed by this dialogue and prayer:
   
   V. Pray for us, O holy Mother of God.
   R. That we may be made worthy of the promises of Christ.
   Let us pray: O God, whose Only Begotten Son,
   by his life, Death, and Resurrection,
   has purchased for us the rewards of eternal life,
   grant, we beseech thee,
   that while meditating on these mysteries
   of the most holy Rosary of the Blessed Virgin Mary,
   we may imitate what they contain
   and obtain what they promise,
   through the same Christ our Lord. Amen.
   
   (A prayer to St. Joseph may also follow.) Conclude the Rosary with the Sign of the Cross.

Source: http://www.usccb.org/prayer-and-worship/prayers-and-devotions/rosaries/how-to-pray-the-rosary.cfm