How do I get a computer microphone to record on my comp.?

So I like to write songs and stuff but the little cette record I have stinks so I got a microphone and some software to record my music nothing fancy just something I can use to not lose all my songs, and something w/ a little higher quality sound, but to my dismay I can't figure out how to get it to work. I'm not the most computer savy person so if some one could go into really detailed instruction about it that would be great. I have an emachine comp. and I plugged the mic.-a radio shack desktop computer microphone- into the back mic plug in but it does nothing...I don't really know what I'm doing wrong so if somebody could please help me that would be great. Thanks alot!