Firstly, download
Audacity.
Secondly, do you have Rock Band or Guitar Hero World Tour? If so, you have a USB mic. You can plug this in, and put it up to your guitar amp, press record in Audacity, and start playing.
If not, you're going to want to pic up a mic and a preamp. If you plan on sticking with recording, I believe an SM57 is the mic you want. (They're like a hundred bucks, but pretty much last forever from what I understand.) If you're on a super tight budget, and you're just recording demos, I personally don't have a problem with radioshack mics. (Others will disagree. If you're just doing demos though, you don't need great sound quality.)
For the preamp, you can just get a small mixer. Check craigslist and ebay. I picked up a little Behringer one for like $50 after shipping, and the next day I saw one sold for 35 before shipping. (No, I didn't get screwed, that one was very far and would have 20 dollars shipping.)
Once you have all that, you're going to need another 1/4" cable, and a 1/4" to 1/8" adapter. (Both very cheap.) Put the mic up to your guitar amp, plug the mic into the mixer/preamp. You plug that into the output on your mixer/preamp, then into your soundcard, and record through audacity.
If you want to start getting into layering tracks and editing stuff, there are a number of free programs out there. Jeskola Buzz, for example, is a good one. It's interface is very different, and takes a bit of learning, but you can get a lot of good synth and drum machine sounds out of it.
Good luck!