By request, I’ve done some looking around for resources related to Proof by Contradiction. I haven’t found a page with a good “big picture” overview yet, but I have found some decent examples – here goes:
Getting started – some basic examples. This page has a few examples worked out completely – not too long or involved, and (I hope) not too difficult to follow.
Numberphile: Proof (by contradiction) that there are infinitely many primes. A really good illustration of proof by contradiction. The numberphile guys make cool math videos – if you like it, search for numberphile and check out their other stuff.