What you need is a mic preamp, first off.

What do you usually use for performing? Nearly all guitar amps have a "preamp out" (either an FX loop out or line out or something), so you could use that. Or use a mixer of some kind. Be warned that PC soundcards generally record at lower levels than PA stuff uses, so check the levels in your recording program.

Then feed the amplified result into the "line in" socket on your PC soundcard. The "line in" is stereo so there are left and right connections - if you're only recording one mic track at a time, it doesn't matter which one you use. You can get connectors from electronics shops (places like Maplin in the UK or Circuit City in the US) which have a stereo mini-jack (3.5mm) on one end and two regular instrument jacks on the other end.

You'll usually get better quality by doing the analogue-to-digital conversion outside of the PC - the inside of a PC is generally electrically noisy - which means getting some external box of tricks like Frank mentions. And by using a dedicated mic preamp instead of just a guitar amp (the external box of tricks may come with a mic preamp, or it may record at line level in which case you'll need a separate mic preamp). You're talking extra gear here though, so it depends on whether what you get with what you've got is good enough. If it isn't, you can spend any amount from around £50 for a basic preamp and USB cable up to thousands for your high-end studio kit.

Program-wise, Audacity (http://audacity.sourceforge.net) is free, and it's good enough for basic recording. Once you start talking multitrack then Audacity starts to fall down, but it's OK for simple stuff.

Graham.