Techknight has an excellent point, especially if you know someone with more expertise that you can take it to for help.
However, if you want to learn a little bit about the inside of the machine, read Larry Pina's Repair and Upgrade Secrets and/or The Dead Mac Scrolls (pdfs are floating around the internet, or physical copies are available from used book services for very reasonable prices) and you'll have a better understanding of what is involved.
Opening the back of the case is perfectly safe as long as you keep your fingers away from anything leading to the CRT. I was comfortable doing things on the logic board for a long time before I worked up the nerve to learn how to discharge a CRT and detach the analog board.
For things like testing the voltage, you would need a multimeter (you can do this without even removing the back, see Larry Pina). If you want to try your hand at replacing caps, that requires a good soldering iron and accessories. I'm hoping to learn more about soldering this summer.
Good luck!