i'm not an Electrial Engineer so if i'm wrong (and i make mistakes too =D) try not to kill me. But i think that the capacitors are usually the "cylindars" on boards and often times are used to regulate electrical current. Often times they do this by acting as a sort of battery storing some juice as electricity zips around the board at 186,000 miles per second.
Traces are the "lines" put down that essentially act as wiring for the board. With the increasing sophistication of these boards often times the traces are put down layer after layer on these PCB boards to enable the complexity which the designs require. Often times you will hear that such and such a card had a 7 layer process etc etc.
Resistors are what they sound like. Often times they look like a small "coil" turned on its side enabling some type of functionality.
With hardware trouble shooting over the years i can typically determine what the hardware problem is on a system within just a few minutes. Usually it is a strong hunch (again from experience) and i validate my assumption by swapping components. If i'm right then great, if not then i keep swapping until i find the weak link. Hopefully your case allows for easy access to "the goods."
Given the cost of mobos, procs, vid cards and ram these days it doesn't hurt to have a few extra items on hand so that if you have problems with your box you can get back into the swing of things in record time.
