The basics are laid out in User-friendly: Analyzing your first BSoD!, but it takes a while to really get the hang of everything. I spent my first few weeks learning what to look for and asking the experienced users questions. I still learn something new just about everyday.

Hopefully we can narrow down which hardware is causing the problem. Hardware debugging is a difficult task given everything that goes into a computer. There are other gurus on here who can help if something comes up that I do not recognize or am not experienced working with, so you're in good hands. :)