The Rosary is essentially the decades and their associated mysteries, and only these must be prayed to "pray the rosary", either in satisfaction of Our Lady's requests, or, to gain the indulgences attached to praying the rosary.
The traditional Rosary is divided into three parts, each having five mysteries: Glorious, Joyful and Sorrowful. In his apostolic letter "The Rosary of the Virgin Mary", Pope John Paul II proposed a new set of mysteries, which he called the Luminous, and which concern the period of the public life of Our Lord. For those who wish to say all 20 decades at once during the course of a day, they may be said in the following order: Joyful, Luminous, Sorrowful and Glorious.
For those who wish to say only 5 decades per day, the Holy Father proposed the following schedule:
For those who prefer to follow the traditional order of the days it is:
While meditating on the Mysteries, recite:
One Our Father (large beads), 10 Hail Marys (small beads) and 1 Glory Be (before the next large bead) to make a complete decade of the rosary.
After each decade the Fátima Prayer may also be said (Pope Pius XII).
O my Jesus, forgive us our sins, save us from the fires of hell, lead all souls to heaven, especially those who are in most need of Thy mercy.