Answer:
We are not told 'how' Judas became a disciple except that he was chosen by Jesus.
This does not mean that Jesus made a mistake in choosing someone who would betray him as he knew from the outset his mission and his fate, and predicted his death and resurrection many times.
What we do know is that Judas was not from Galilee (Iscaria is not in that area) and was the 'keeper of the purse' i.e. the disciples' 'treasurer'. However, John's account tells us that he often helped himself to money from the common fund; whether this is actually so or whether it is John's character assassination, we don't know.
In recent times there have been moves to make Judas into a saint. The reason for this was that, as Jesus' betrayer, it can be argued that Judas was doing God's work to bring about Jesus' death and resurrection and, consequently, our salvation. Although controversial, this idea fits well into the reasons why, presumably, Jesus, as an expert in other peoples' characters, chose Judas in the first place.