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.
Step 2: Mix the dyes
you have some dyes that are water-soluble. If you just squirt them on a shirt, they'll wash off. However, if you treat the shirt with a fixer, it'll hold the dyes in place. In our case, urea is our fixer.
I really like mixing my dyes in ketchup-style squirt bottles, which makes for easy dying. However you choose to do it, add some warm water to a container, and then mix some dye powder in. I do it qualitatively--the more dye you add, the brighter the colors will be, although there is some saturation point. A good rule of thumb might be 1 tablespoon of dye for 8 ounces of water.
Anyway, put some dye into the water and mix it up. Then, go on to slep 3