His story of conversion is set as he is on the road to Damascus and is knocked from his horse where he meets Jesus. Read more about his story of conversion as he becomes one of the greatest defenders and spreaders of the Gospel.
Most of the New Testament that isn't the Gospel is from Paul's letters to the various churches he set up during his travels.
Scott Hahn tells the story in this short 12 minute video: http://youtu.be/OXk7a3blph4