This is really easy in theory...just writing with bleach, but it takes a steady hand and much patience.
So this is pretty self-explanatory. Just get a bowl, pour in a little bleach and grab your brush.
You should also but the cardboard between layers of your shirt, so that the bleach doesn't bleed through to the other side.
I would advise you to use chalk or pastels to do a rough version of your design first, even if you're just doing text or whatever.
Paint carefully, it's easy to go outside your lines, or not to get enough bleach on them. Don't get the brush so soaking with bleach that it drips, because it'll drip on your design.
I didn't have a watch out there with me, because I did this outside (which YOU should do too...the fumes, oh god) but it's really obvious when the bleach starts to change the color of the shirt.
After your design is finished being bleached onto the fabric (after the bleach is done bleaching)dunk it into your bucket of water and rinse the bleach out. Allow to dry.