Luke 5:1-11, 5:27-32; John 1:35-51
In addition to the story recorded in Luke 5, the other three Gospels also record various aspects of Jesus calling and appointing his disciples. We encourage you to read these accounts as well:
The Luke account is a good one to focus on with the kids because it contains a wonderful and memorable story.
Jesus is preaching by the Sea of Galilee (Luke calls it the Lake of Gennesaret) and he notices two boats that had been left there by some discouraged fishermen. Simon, James and John were fishing partners and they had a tough night of fishing. They worked hard and didn't catch a thing. So they had hung it up for the day and they were cleaning their nets.
Jesus asked them if he could use their boats to preach from since there were so many people. Simon Peter agreed and took him out just a little bit into the water. Jesus finished preaching and told them to put out into deep water again and let the nets down for a catch. Simon told him that they had just worked all night and didn't catch a thing, but "because you say so, I will let down the nets". They heard the words of Jesus and knew there was something special about him. So they had enough faith to do this thing he asked them to do, even though they didn't have any expectation that it was going to actually work.
But when they let down their nets, they caught such a huge catch of fish that their nets began to break. They had to go get help to bring in the amount of fish they had caught without sinking their boat.
Simon Peter was terrified at the power this Jesus displayed and fell on his knees and said, "Go away from me Lord; I am a sinful man!". But Jesus told him not to be afraid and that from now on, they will catch men. So those 3 men left everything they had - their boats, nets, and fishing business - and followed Jesus. They became some of the first disciples of Jesus.
Through the other accounts in the Gospels and the rest of the New Testament, we learn that these 12 men become Jesus' closest friends and disciples. Jesus was closest with Peter, James, and John.
Here are the names of the 12 disciples (Mark 3:16-19 gives a listing):