The conversion of Saul is one of the classic, dramatic conversion stories in the whole Bible. Saul has to travel as far as one can possibly travel to become a Christ follower. Saul was in training to be a Rabbi. He served as the official approving witness at the stoning of Stephen. He then set his sights on destroying the fledgling Christian movement, getting permission from the Sanhedrin to arrest any and all who were followers of the "Way". Persecuting the church in Jerusalem was not enough for Saul he got permission to travel to Damascus and persecute the church in that location as well.
Bright lights and a voice from heaven stop Saul in his tracks. He hears a voice ask "why are you persecuting me?" and when Saul asks "who are you?" the voice says "I am Jesus . . ." Saul, when he arises, is blind and the powerful persecutor is now powerless and must be led by the hand into Damascus. Saul fasts and prays and waits for three days before God sends a Damascus disciple named Ananias to pray for him that he might receive the Holy Spirit and his sight. Saul immediately begins to preach the Gospel. What happens next is going to be a recurring theme in all of Saul's ministry: people try to kill him. He escapes in the night and travels to Jerusalem where the Apostles refuse to meet with him until a man named Barnabas (his name means Son of Encouragement) introduces him around.
I have often thought that the drama of one's conversion is about how far we have strayed. For many people, even if they hadn't chosen to be Christ followers, they were still fairly good people trying to live good lives. These people, when the choose Christ, do not often have dramatic experiences. Typically it is more of a general awakening, a realization of a new life. For others of us who strayed a long way from the truth or, as in Saul's case, were actively working against the cause of Christ the journey back is radical and dramatic. Saul's conversion is one such instance. Remember that Saul was his Hebrew name. He uses another name out in the "Greek" world. He was known as Paul.