A few things you'll need:
-Gloves (it gets dirty)
-Extra latex glove
-Cone wrenches that match your hub. Most are 13mm and 17mm, but they vary.
-Toothbrush (preferably your roommate's)
-Towel (preferably a clean washcloth, but paper towels are probably best since it'll be ruined the moment you use it)
-A clean, open workplace where you can find loose bearing balls that shoot off into the nevernever
You'll need some kind of cleaner for the grease, but I left this out because you can use damn near anything. The bearing balls are stainless steel, so you're not going to hurt them. I've used WD-40 for as long as I can remember, but I used windex this time and it worked fine. Residue isn't a real problem because you'll wipe them down on the paper towel before you put them back in.
Step 1: Get in there!
The axle is not held in with anything except those cones, so once you start to loosen them up, the bearing balls can fall out. The dust cover helps, but not all hubs have them and even with them the balls can fall out. You'll want the wheel sitting on the table while you do this so the axle is always pressed into the hub.