The three Synoptic Gospels record the circumstances in which some of the disciples were recruited, Matthew only describing the recruitment of Simon & Andrew and James & John. All three Synoptic Gospels state that these four were recruited fairly soon after Jesus returned from being tempted by the devil.
Simon and Andrew are, according to Matthew, the first two apostles to be appointed, and Matthew identifies them as fishermen. Mark does not identify Simon as also being called Peter until a long time after Simon is introduced in the narrative, but Matthew immediately makes the connection as soon as he is first mentioned.
This has the effect of changing the later passage where Jesus names Simon as Peter from one where Jesus bestows the name onto Simon into one where Jesus merely starts using a long held nickname.
Both Andrew and Peter are names of Greek origins, which France sees as a reflection on the multicultural nature of Galilee at this time, although evidence exists that Andrew was used by Jews as a name since at least 169 BC in the early period of Hellenic influence. Simon however is the Greek form of the Hebrew name Shimeon, a common Jewish found referring to several other individuals in contemporary works such as Josephus as well as in the Old Testament.
Despite Jesus only briefly requesting that they join him, the two are described as immediately consenting, and abandoning their nets to do so. Traditionally the immediacy of their consent was viewed as an example of divine power, although this statement isn't made in the text itself.
The alternative and much more ordinary solution is that Jesus was simply friends with the individuals beforehand, as implied by the Gospel of John, which states that Andrew and an unnamed other had been a disciple of John the Baptist, and started following Jesus as soon as Jesus had been baptised.
As the son of a carpenter, it is eminently plausible for Jesus to have taken his father's trade, and been employed to build and repair fishing vessels, thus having many opportunities to interact with and befriend such fishermen.
Albright and Mann extrapolate from Simon and Andrew abandonment's of their nets, that Matthew is emphasising the importance of renunciation by converting to Christianity, since fishing was profitable, though required large start-up costs, and abandoning everything would have been an important sacrifice. Regardless, Simon and Andrew's abandonment of what were effectively their most important worldly possessions, was taken as a model by later Christian ascetics.
Matthew describes Jesus meeting James and John, also fishermen and brothers, very shortly after recruiting Simon and Andrew. While Matthew identifies James and John as sons of Zebedee, who is also present in their ship, Mark makes no such proclamation. Luke adds to Matthew and Mark that James and John worked as a team with Simon and Andrew.
Matthew states that at the time of the encounter, James and John were repairing their nets, but readily join Jesus without hesitation. This parallels the accounts of Mark and Luke, but Matthew implies that the men have also abandoned their father (since he is present in the ship they abandon behind them), and Carter feels this should be interpreted to mean that Matthew's view of Jesus is one of a figure rejecting the traditional patriarchal structure of society, where the father had command over his children; most scholars, however, just interpret it to mean that Matthew intended these two to be seen as even more devoted than the other pair.
The synoptics go on to describe that much later, after Jesus had later begun his ministry, Jesus noticed, while teaching, a tax collector in his booth. The tax collector, Levi according to some Gospels, Matthew according to others, is asked by Jesus to become one of his disciples.
Matthew/Levi is stated to have accepted and then invited Jesus for a meal with his friends. Tax collectors were seen as villains in Jewish society, and the Pharisees are described by the synoptics as asking Jesus why he is having a meal with such disreputable people. The enigmatic reply Jesus gives to this is now well known: it is not the healthy who need a doctor, but the sick ... I have not come to call the righteous, but sinners.