Testing components is a very important part in radio repair. Test equipment can get a bit pricey. As LC mentioned you can check transistors and diodes with a simple analog volt meter or a digital volt meter. A lot of times you will have to pull the device out of circuit to test it. I use an old RCA transistor tester to see gain. But most of the times it is my old analog meter I check with. I will also show you a simple way to build a transistor tester. With only a handfull of parts.
9 volt battery and clip.
68 ohm resistor
56k ohm resistor
led
N.O. push button switch
Red test clip
Green test clip
Black test clip.
Small case to house the components
You should still be able to find most of these parts at your local radio shack.
This is a good way for quick checks on transistors.