It depends largely on what kind of music you want to make. If you're talking rock or anything else using mostly real instruments the list will be long and expensive. If, however you want to create something electronic in nature, you could do quite nicely with this:
1: Reasonably fast computer, preferably with at least 1GB RAM.
2: Some kind of keyboard with MIDI and USB capabilities, which would enable you to play software instruments on said computer. You can get these real cheap, 100-200$.
3: Audio interface(external soundcard). The audio-in port on your computers soundcard SUCKS, so unless you're sure that you will never, ever, need to record something you'll need one of these. Behringer makes some really cheap ones, Presonus or Lexicon has the good but expensive models. Well, actually, i use a 90$ Behringer box and while it's far from perfect it records my voice and guitar with reasonable accuracy.
4: Microphone. The Shure SM57 is nicely priced (100-150$) and can record pretty much anything.
5: Software. Expensive, but you're nothing without it. I use Mackie's Tracktion, it is extremely easy to use while still offering a lot of advanced functions and comes with a bunch of virtual instruments. 300$.
6: Good speakers. No point in getting a lot of fancy gear if you can't hear what you're doing.
I've probably forgotten something, and this is obviously just a basic home studio, how to actually write a song is a completely different matter and takes a lot of time and effort. Oh, and on the off chance that you're a Mac user there's a neat little preinstalled program called GarageBand which is a lot of fun.
Anyway, i hope this has at least pointed you in some kind of direction. Making music is both time-consuming and at times expensive, but also very satisfying and fun.