So I got Audacity for my computer. But here's the problem, I have nothing to plug my amp in so it can go through to the computer. I tried to plug in a cord to my amp from the computer, but it wouldn't work.

You are going to need a microphone, unless your amp has a direct output like the Line 6 amps that are commonly sold to beginners. Those come with instructions. Google "recording basics" and try to understand the general concept of how recording works for a start.