546. How did Peter and Andrew become Jesus's disciples?

Jesus called them directly as they were fishing on the Sea of Galilee.

As he walked by the sea of Galilee, he saw Simon and Andrew his brother casting a net into the sea: for they were fishers.

And Jesus said unto them, Come ye after me, and I will make you to become fishers of men. Mark 1:16-17

Jesus, walking by the sea of Galilee, saw two brethren, Simon called Peter, and Andrew his brother, casting a net into the sea: for they were fishers.

And he saith unto them, Follow me, and I will make you fishers of men. Matthew 4:18-19

They were with John the Baptist and approached Jesus on their own.

The next day after John stood, and two of his disciples ... One of the two which heard John speak, and followed him, was Andrew, Simon Peter's brother.

He first findeth his own brother Simon, and saith unto him, We have found the Messiah, which is, being interpreted, the Christ.

And he brought him to Jesus. And when Jesus beheld him, he said, Thou art Simon the son of Jona: thou shalt be called Cephas, which is by interpretation, A stone. John 1:35-42

Jesus called Peter after nearly sinking his boat by catching so many fish for him.

(Luke doesn't say how Andrew was called.)

When he had left speaking, he said unto Simon, Launch out into the deep, and let down your nets for a draught.

And Simon answering said unto him, Master, we have toiled all the night, and have taken nothing: nevertheless at thy word I will let down the net.

And when they had this done, they inclosed a great multitude of fishes: and their net brake.

And they beckoned unto their partners, which were in the other ship, that they should come and help them. And they came, and filled both the ships, so that they began to sink. ...

And when they had brought their ships to land, they forsook all, and followed him. Luke 5:4-11