Simon is all over this one with great advice!

I second getting yourself a DMM (Digital MultiMeter).
Not only are they invaluable for troubleshooting, but are a great way to learn about signal flow in guitar circuits.
It helps to kind of "visualise" where the signal goes from one component to the next.

I prefer DMM's that have an audible beep for continuity testing rather than having to watch the screen to zero out.
Like SB said, they're not very expensive and you'll be surprised how much you use one for other things once you get one. (like checking battery voltage)