Begin with an Act of Contrition:

O, my Lord and Savior, Jesus Christ, behold me before your divine presence, all in confusion at the thought of the many grievous injuries I have done you. I ask pardon for them with my whole heart, repenting of them for love of you, hating them above every other evil and ready to lose my life rather than offend you again. And do you, most tender Virgin, mother of mercy and refuge of sinners, obtain for me the pardon of all my sins by virtue of your bitter pains and help me to so pray as to gain the indulgences attached to this, your most holy Rosary.

Come, Holy Spirit, fill the hearts of your faithful and enkindle in them the fire of you divine love. Send forth you spirit and they shall be created and you shall renew the face of the earth.

Enlighten our minds , we beseech you, O Lord, with the light of your brightness, that we might see what we ought to do and be able to do what is right, through Christ, Our Lord.

Then proceed through the devotion in this manner:
Announce the Sorrow; then devoutly pray the Our Father
Slowly, reverently, pray seven Hail Marys while meditating on the Sorrow.
Repeat these two steps continuing through all seven Sorrows.

At the end of all Seven Sorrows, three Hail Marys are said in honor of the Tears of Our Sorrowful Mother.

Our Father, Hail Mary, and the Gloria, for the intention of our spiritual superiors.
Reverently ask Mary three times: "Virgin most Sorrowful, pray for us."

Those are the verbal mechanics of the devotion. But all rosaries are a mixture of vocal and interior prayer/meditation.

Meditate on the following while reciting the prayers

The First Sorrow:
Let us meditate on the first Sorrow of the Blessed Virgin, when she presented her only son in the temple, laid him in the arms of holy Simeon, and heard the prophetic words, "This one shall be a sword of sorrow to pierce your own heart."

The Second Sorrow: Mary flees into Egypt with Jesus and Joseph- Forced to endure the hardships of a long journey, and becoming a foreigner in a strange land, Mary and her family flee to protect the child Jesus from those who would destroy him.

The Third Sorrow: Mary seeks Jesus lost in Jerusalem- Jesus disappeared for three days in Jerusalem at the age of twelve, causing his parents, especially Mary, agonizing sorrow.

The Fourth Sorrow: Mary meets Jesus on the way to Calvary- As Jesus makes his way to Calvary, condemned to crucifixion, He meets His mother, Mary. He is bruised, derided, cursed and defiled and her sorrow is absolute as Jesus drags His own cross up the hill of His crucifixion.

The Fifth Sorrow: Mary stands near the cross of her Son- Mary stands near her dying Son unable to minister to him as he cries "I thirst". She hears him promise heaven to a thief and forgive his enemies. His last words, "Behold your mother," charge us to look on Mary as our mother.

The Sixth Sorrow: Mary received the body of Jesus taken down from the cross- The passion and death are over but for his mother, grief continues. She holds His body in her arms.

The Seventh Sorrow: Mary places the body of Jesus in the tomb, awaiting the resurrection- The most tragic day in history ends, Mary alone in sorrow, as she lays the body of her Son, in the tomb.

We hope that this devotion brings you ever closer to Jesus, through Mary. God's richest blessings be upon you.