A computer and a half decent soundcard, though you can have a lot of fun even with only a Soundblaster or similar (I worked for at least two years on that kind of setup, no matter what people say).
Then you need a sequencer of some sort. A lot of people find Reason a good starter because it has all the synths, drum machines, basic effects, samplers etc. that you will need to begin with, for a decent price and very user friendly.
I also helps you to understand how real hardware equipment works as it mimics it fairly successfully (you can even mess around with the wiring behind the fake rack).
That should give you a lot to start with. The downside is that it doesn't do any audio...
Buying a more advanced sequencer program like Logic or Cubase might confuse you unnecessarily. I started working with Audio only (i.e. I had hardware to record into the computer) and used Cool Edit Pro which got me a long way before I decided to move into the real production world.
Hope that helps. There's lots of people on this forum that'll give you pointers along the way if you ask.
Have fun!!