Your best troubleshooting tool is your brain.
The best way that I'm aware of is to find someone who is good at it, then learn from them.
Learn to ask questions like these: Did it work correctly in the past? If so, what has changed? (Install/design problems for something that has never been right are a whole different set of clues than something that's been running for years...)
A big part of electrical troubleshooting is truly understanding how the components work and interact. Learn to read the electrical drawings -- they're your best friend.
Learn to understand the PLC program in a PLC-based machine -- it's one of your best diagnostic tools. And learn that the program didn't "change itself" (You wouldn't believe how many times I've heard that one...)
BUT learn to NOT change to program when working on a program. Sure, you can possibly code a patch to get around the problem, but you haven't fixed it. Writing patch-code will almost always introduce a whole new set of unintended problems.
Learn that most electrical problems are really mechanical problems with electrical symptoms. Motor heaters tripping out are usually mechanical (if the system has been running for awhile and they were properly sized}. A tripped circuit breaker really means something mechanical like a physical connection. A blown fuse should always be replaced with the same size/type of fuse -- that fuse was sized by the designer for a reason and bypassing that design will cause other problems. Always physically check a sensor that "isn't working" because it's probably been moved/bumped.