Sorry, I didn't see that the question had already been asked on the main site. As Felipe says, my reply above doesn't really add anything, so I don't see any need to post it there. (But I don't think you did anything unseemly!)

Best wishes,

Matt

Get a copy of the book "Modular forms and Fermat's Last Theorem" and read it. It remains the best introduction to this part of mathematics (unless you are in the situation of having an expert at hand to teach you directly). You will want to read a lot of other things for background as well, unless you know a lot of number theory already. My guide to learning Galois representations (should be easy to find on the main site) gives one possible approach.

Regards,

Matthew

P.S. There is also the excellent paper of Darmon, Diamond, and Taylor. You could read that in conjunction with the BU volume. I don't think there is any advantage to going via the Serre's conjecture literature. Many of the key ingredients are the same, but the proof of Serre's conjecture (since it is proving a more general result) is harder going at various points, and requires more input from the theory of automorphic forms.

I don't think this question should be community wiki, because to answer well, as Andres has, is a demanding task.

It's not necessarily applicable to every roadmap, but it's something to take into account. (On the other hand, no one on MO cares about reputation... :-))

More seriously, there is also the more recent proof by way of Serre's conjecture. Experts would be able to say which of the proofs is easier, and which is more profitable to spend the time tackling.