Its real easy.
You'll need:
1. A pot and a heat source to "boil" them in.
2. I'd get some sal-soda, also called washing soda.
3. Dawn detergent, concentrated variety is best.
4. 40 volume creme developer from a beauty shop along with some basic white or magnesium carbonate.
First step will be to mix in a cup or two of sal soda into the water, DONT boil your skulls and try to keep the deer antlers out of the water as much as possible. The antelope, I'd submerge just below the prongs. You'll have to pop the antelope horns off the skull. Usually takes about 20-30 minutes in hot water before they slide off. Once the horns come off simmer for maybe 2-3 hours...again DO NOT boil.
Much of the flesh will start coming off at this point, scrape what you can, and just keep letting the skulls simmer until you have them clean.
Next, I start with clean water and about half of a large bottle of dawn dish soap. I simmer the skulls for another 4-5 hours in that, a majority of the grease will be gone from the skulls. Repeat that process if you arent sure if the grease is gone.
Once the skulls are at that point, mix a thick paste from the basic white/magnesium carbonate and 40 volume creme developer. Paint them with the paste, covering liberally, but keep it off the antlers. I usually wrap the bases of the antlers with aluminum foil to ensure the paste doesnt get on them. I then wrap the skull with a plastic bag and leave them for 3-4 days. Open them up, rinse off the paste and let them dry.
You'll have to use some bondo and re-attach the antelope horns to the skull once its cleaned and bleached.
Come out pretty good generally.
These are the skulls I did from the animals my wife and I shot last year:
Some of our antelope as well from the last 10 years or so:
My wifes 2010 booner antelope:
