Start with the manual. From there, locate the information for fuses (number one thing you'll find as an indicator of a problem). The manual will help find more common issues.

The best rule of thumb is to logically isolate areas that could potentially be a problem (if you have a specific symptom). i.e. if you have a fuse blowing, try to isolate parts of the circuit it is powering to locate the problem area. Deduce by process of elimination.

Certain problems are pretty obvious and don't require a lot of troubleshooting skills. Burned coils will pretty much always mean a new coil and replacement transistor(s) at minimum. Unless it's a flipper coil.

If you have advanced problems (board level, CPU, etc...) the best suggestion is to be patient, take your time and do lots of reading. I took 2+ years of electronics training and worked in the field on Pinballs for a living for almost 5 years before leaving the profesion. You're not going to pick up advanced electronics skills overnight. But, there's nothing in a pinball that anyone can't figure out either.

Hope this helps (at least a little).

G