The Rosary is both a mental prayer and a vocal prayer.  It is a mental prayer when we meditate on the mysteries.  The vocal prayers are the Creed. the Our Fathers, Hail Maries, the Glories Be and other prayers we articulate.

The Rosary always begins with the Sign of the Cross.

In the American English version of the Rosary, The Creed is prayed next , followed by an Our Father , three Hail Maries  and a Glory Be.   The first Hail Mary is dedicated for an increase of Faith.  The second  Hail Mary is dedicated for an increase of Hope  and the third Hail Mary is dedicate for an increase of Love (This may vary from one culture to another.  In some Latin American countries, these prayers are said after the Mysteries of the Rosary, just before the Hail Holy Queen).  

Next follow a set of Mysteries or a Decade.  There are three Decades to choose from; The Joyful Mysteries, The Sorrowful Mysteries and The Glorious Mysteries.  You may choose a to pray one Decade, or you may pray all three Decades in that order.

There are five Mysteries on each Decade, making it a total of fifteen Mysteries. The Mysteries are biblical accounts on the life of Christ and Mary.  

The Joyful Mysteries are  five accounts on Christ early life.  They are, The Conception of Christ also known as The Annunciation of the Angel, The Visitation of Mary to her cousin Elizabeth, The Birth of Christ also known as The Nativity, The Presentation of the Child Jesus on the Temple, and The Finding of the Child Jesus on the Temple among the Doctors of the Law.  These accounts are refered as Joyful because they brought joy to Mary's Immaculate Hearth.

The Sorrowful Mysteries brought sorrow to Mary's Immaculate Hearth.  They are five related accounts on the Passion of Our Lord.  The First Sorrowful Mystery is Jesus Praying and Suffering at the Garden of Getsemani.  The Second Sorrowful Mystery is The Scourging of Jesus Chained to a Pillar.  The Third Sorrowful Mystery is The Crowning of Jesus with a Crown Made out of Thorns.  The Fourth Sorrowful Mystery is Jesus Carrying his Cross.  And The Fifth sorrowful Mystery is The Crucifixion of Jesus.

The Glorious Mysteries refer to five events that are the result of Christ's victory over the forces of evil .   The First Glorious Mystery is The Resurrection of Christ after his Crucifixion.  The Second Glorious Mystery is His Ascension into Heaven.  The Third Glorious Mystery is The Decent of the Holy Spirit upon the Apostles on the day of Pentecost, also known as The Birth of the Catholic Church.  The Fourth Glorious Mystery is the Assumption of Mary into Heaven.  And on The Fifth Glorious Mystery, Jesus Crowns His Mother as Queen of Heaven  and Earth (under the authority of Jesus, Mary obtains the highest place in Heaven any creature may have).

Each Mystery is prayed as follows:

First announce your Decade (e.j. "The Sorrowful Mysteries") and then announce the first Mystery of the Decade (e.j. "The First Sorrowful Mystery, The Agony at the Garden").

Per each Mystery you pray an Our Father followed by ten Hail Maries, one Glory Be, an depending on you local region or own tradition you may add a short prayer.  The O My Jesus prayer is the proffered in the United States.  You repeat this for each Mystery you pray.

If you decide to pray another Decade, introduce the new Decade and the First Mystery of that Decade.  Then, pray each of the five Mysteries of the new Decade as explained before.

The last prayers are then recite.  They are The Hail Holy Queen and The Ending Prayer.  Finally, an Our Father, a Hail Mary and a Glory Be are offered for the intentions of the Holy Father.