The Holy Rosary is a traditional Christo-centric Marian prayer; that is, a prayer centred on Jesus through Mary. Through the recitation of decades - a set of 10 Hail Mary, begun with the Our Father, and ended with the Glory Be - we keep track of our prayers most notably by use of rosary beads. Crucially, we contemplate on the mysteries in the life of Jesus Christ and His Blessed Mother.
The Church divides the mysteries of Jesus' life into three sets of five decades:
The Joyful Mysteries
The Sorrowful Mysteries
The Glorious Mysteries
In 2002, Pope St. John Paul II in his Apostolic Letter Rosarium Virginis Mariae recommended that a new optional set of mysteries be prayed on Thursdays, which are the Luminous Mysteries so that 'in the course of those mysteries we contemplate important aspects of the person of Christ as the definitive revelation of God.'
The Luminous Mysteries
We pray the Rosary together in the Chaplaincy, usually on a Sunday.
The Church recommends to us that we take one set of mysteries at a time, and spread them across the week, so that (if we are praying the Rosary daily) we cover all of them twice over the course of a week.
The traditional cycle is:
Monday - Joyful Mysteries
Tuesday - Sorrowful Mysteries
Wednesday - Glorious Mysteries
Thursday - Joyful Mysteries
Friday - Sorrowful Mysteries
Saturday - Glorious Mysteries
Sunday - Joyful Mysteries in Advent and Christmastide, Sorrowful Mysteries in Lent, Glorious Mysteries in Eastertide and Ordinary Time
You can, though, always select any set you wish. You can also pray one decade, two, five, or all fifteen (as recommeded by St. Louis de Monfort) if you wish!
Just remember - one mystery said with devotion, is worth fifteen said without.
More information on the Rosary (including solid reflections) can be found here.