In the Catholic tradition, what happens to one who grew up a faithful Catholic, apostatized, and then later returned to faith? What would the process of returning to the church look like? (i.e. Would they need to be re-baptized? Would they have to go through RCIA?)
No, they would not be re-baptized (unless there was doubt about the validity of the first baptism, in which case he would need to be conditionally baptized).
In the case of a public apostate, it would be prudent for a bishop to issue a public letter making the ex-apostate's reversion known to all, so as to avoid the possibility of scandalizing those who might think he is still excommunicated. Oftentimes, the penance for a public sinner is public, so his reversion could be manifested that way as well.
As Geremia said, they would not (indeed, could not) be re-baptized if their original baptism was (known to be) valid. The main thing the returning Catholic would have to do is to make a good confession. The priest hearing the confession would be able to decide whether anything more needed to be done, for example to repair any scandal that the apostasy might have caused.