I have been doing this for a while now. I have done several for myself and my friends, all with good results. It is a messy and stinky undertaking, but the end result is worth it.
1. Skin out the head removing as much meat as possible. When I say "as much as possible" I mean every little scrap you can get off. This will make the boiling step MUCH easier.
2. Unwrap a wire coat hanger, or simply find about 8" of very stiff wire. Insert this into the base of the skull and "scramble" the brain until it's mush.
3. Pick the brain out with a pc. of wire that you have made a small hook on the end of. If you have access to an air compressor and a blow nozzle, this part goes much faster, BUT it is also MUCH messier. Get the skull cavity as clean as possible using either method.
4. Using a turkey/fish fryer and a pot that is ONLY to be used for this stuff, bring a pot of water to a simmer. I add soda ash when I can get it, but a small amount of de-greasing dish soap works fine too.
5. Add your skull to the simmering soap water. If the water comes up on the bases of the antlers, remove it and wrap them with aluminum foil and then cover the foil with a plastic sack, securing it with duck tape.
6. Simmer your skull for 3-5 hrs. adding water and soap as necessary until it is completely free of all meat, brain, and sinew. Using a stiff bristle plastic brush expedites this process.
7. Spray your clean skull off with a hose, pressure washer, or take it to the car wash. If using the pressure washer or car wash, understand that you need to be careful. High pressure can and will damage the skull.
8. Once cleaned and rinsed, allow the skull to completely dry for at least a week. Stuffing it and wrapping it with paper towels helps, just make sure to change them out periodically.
9. Purchase high strength peroxide from any beauty salon, either in liquid or powder form. I prefer powder so I can make a paste.
10. Place liquid peroxide in a container large enough to hold the skull, once again, this is not something you want on the antlers. I make a fairly thick paste and apply it all over the skull using a popsicle stick. Either way, make sure the skull is covered with the peroxide.
11. Depending on how well you cleaned it, the skull will need to be in the peroxide approximately 2-5 days.
12. Once the skull is clean and white, remove from the peroxide and rinse with water.
13. Allow to completely dry for at least a week.
14. At this point you should have a nice, white skull, free of any debris or odor. You may still have some "blotchy" areas that had unusually high fat stores or that simply didn't have enough time in the peroxide. You can either go through the peroxide step again, or if you want a very white, even colored skull, you can give it a light coat of Kilz primer in the spray can.
This is a fairly old photo, but it gives a pretty good idea of the results.
Good luck and feel free to PM me with any other questions.