Step 1: Things you'll need
Cotton shirts (silk works too, polyester is the problem fiber)
Rubber bands or other tying implements
So, tye-dying is really simple. All you need are some dies, a fixer, some fabric, and something to do the tying with.
I like the Procion Dyes--They're very bright and are easy to mix. You can get them online, or at your local art store. Get a bunch of colors
You'll also want urea. You can get a bag of this at your local art store--it usually comes as a bag of these small white balls
Get some kind of fabric to die--100% cotton works best, bust silk works too, and denim does, to some extent. Polyester, rayon, and the like won't work at all.
Finally, get some rubber bands or twine.