You will have to use a line level output from the amp to go into the computer input, preferably with it's own level control. I probably wont sound very good though. Make sure you dont use a speaker output into your computer.
You need a soundcard (like a Delta 44) a preamp (here you can spend anywhere from $120 -- M-Audio Audio Buddy up to 3 grand, this is the source of hundreds of topics on this forum) and a mike. (Shure SM57, good entry level you'll never outgrow)