Since most musicians have to use electricity to perform in one way or another, learning how to use an ohm meter or these days a multimeter, you can save time and money.
And even more important you can understand your equipment better and get better use out of it.
Getting started is not that hard at all. Just get your hands on a multimeter and start learning how to use it. There's a gazillion books, hit the google search god or just read the instructions that came with your multimeter.
WORD OF WARNING: Stay away from reading AC electricity or high voltage of any kind until you know what you are doing. Not listening to this advice can cause damage to you and your equipment.
But, just learning how to use resistance reading, the part that says ohm (look it up for definition and origin).
Here's a simple example. Let's say your guitar/effects/amp setup stopped working. Take your multimeter, put it on ohms audible, and place one probe on the end of the input jack of the guitar cord. Take the other probe and place it on the tip of the other guitar jack of the same cord. You hear the audible beep, it's continuous.
You know that connection is good. Now slide the probes past the tips to the barrel of the plug and repeat.
What's your findings? If still beeping you know that cord is good. Now do it to the cords between the pedals or the cord from the pedals to the amp. What's your findings? If perform a reading and no beep, you've found your open cord.
You unscrew the covers on the jack and 9/10 of the time you will see the wire pulled from the jack. If not then the cord is cut somewhere in the line, eyeball it. You can usually see it.
Some of you by now are saying, "dude, I'm in the middle of a show, I'm not doing this stuff. Me or my rodie have switched out cords and guitars by now." And yes this is the way to go.
What I'm pointing out here, is when you have the time. Take these readings and even know it's basic 101 stuff, it's really the beginning point of reading complex circuits. Because sometimes when an amp that is dead, it's nothing more than a broke or loose wire that an ohm meter can find quickly.
But you're not ready for that yet, so you start with the basic stuff. Because the unwritten code of techs is to get into equipment and repair it without causing more damage and that takes experience.
So when people ask me how to get started repairing music gear. I tell them if you're a complete rookie, then this is the starting point.