1) I echo all replies about unplugging it.
2) Like @Gotemwill mentioned, use the schematics. Trouble shooting paper is worth while. At worse you'll spend a few hours refreshing you mind about the components in question.
3) I echo @JudeRussell and handiness of wooden chopsticks and the like.
4) Know a hack job when you see it. We have the web and YouTube, so use them. See @rolf_martin_062 story on the Sky Lab thread.
5) This is implied in many responses but I'll spell it out... Take your time. The tortoise wins the race. I recommend a little journal about your pin or project. It's useful to know where your head is at or possible theories about the situation. Especially when real life interrupts you. And handy for general maintenance reminders or that strange hum or to keep an eye on that left pop bumper.
6) I'm surprised this hasn't been mentioned so this is my real 2 cents... Bread boarding. Most engineers use it for prototyping but its useful for trouble shooting. Rig up a piece of ply with the offending components and test/tweak outside the rats nest. A good switching power supply is useful. Coils rated for 50vdc will still energize with 5vdc albeit with delay and much less vigor. Depends on what you're trouble shooting, timing issue are probably best left on the play field. Take pictures/movies and toe tag everything during the process. Don't trust sticky notes or your memory.