I have used a POST card in the past. They're pretty handy. Other than that, the only thing you need is a meter.
Let's look at a typical scenario;
Press power button - nothing --> start by checking power supply.
Press power button, all fans and drives spin up --> Power suppply probably all right
No video / no post beeps --> seat cards, test power supply
Post beeps --> Cross-reference post beeps against the motherboard, usually will tell you what's going on.
Listening is your best tool. If a hard drive is "clunking", and the machine won't boot, you've probably got a failing hard drive. If you complete POST tests, you can start looking at software issues, etc.
I have found that just doing stuff like swapping the RAM in the sockets will help diagnose memory issues, and so forth.
A POST card will show you the POST codes as they're happening, but I don't usually need one.
Just my 2¢
-Cole's Law: Shredded cabbage
--Greg