Well, I assume you're going to want to have multiple tracks, so you'll need a multi-track recording program.
A cheap, easy to use one is N-Track, which can be download for free and registered for a few bucks.
www.fasoft.com
At the higher end of the spectrum would be a program like Cubase, which costs around $500 or so.
Next you need a way to capture whatever you're recording, by which I mean a microphone. You can choose between a condenser or a dynamic microphone. Most people prefer a condensor for guitar & vocal recording. If you go that route, you'll also need a phantom power supply and a preamp.
Those items will be enough to start recording your songs. As you learn more about recording and mixing, you'll definately need a palette of effects to enhance your tracks, such as compression, reverb, chorus, delay, etc...N-Track and Cubase have these equipped.
It really all comes down to how much you can spend, and what quality of recording you are satisfied with. The answer to both, for me at least, is: Never enough
