Audacity. It's freeware. I've never used it, but hear excellent things. It's along the lines of Garageband which comes with Macs. Audacity works with both Windows and Mac.

My advice is to save a little money for a microphone and audio/digital converter to plug it into. No need to spend a lot of money on a microphone if you're just starting out. About $100 on a Shure SM57 or 58 should do it until you learn more :-)

Best of luck!