A disciple (mathetes) is a student, or a learner. Jesus Christ gathered many disciples, traveling for several years with 12 men. He taught them personally, and they passed on his teachings to others. Each Christian is to be considered a disciple of Jesus.
If you ask a bunch of people how they came to faith in Jesus, you'll hear a bunch of different stories. No two explanations are exactly alike. Still, it's helpful to understand what all of those stories might have in common.
