First off decide if you want the lower jaw aswell....most people dont but if you do now is a good time to decide. Using a knife remove as much meat as possible including the eyes. Now take a stiff wire and scramble the brain thru the little hole in the underside of the skull. When its scrambled enough a garden hose will wash the now liquid brain out. Now I know loads of "do-it-yourselfers" and taxidermists "boil" skulls but it is not recommended for a first rate job. Its faster than other methods but it has lots of draw backs. Oh and before I forget you dont actually boil the skull but rather simmer it. Boiling will make many of the joints seperate, often the nose bones fall off and the nasal bones are usually ruined trying to remove the sinus. It also cooks the grease in, and makes the bone brittle if over done. But if you insist, add maybe a tablespoon of Sodium Carbonate per gallon of water. This will help remove the meat and may start to help the whitening process, it is also a good idea to add a clear dishwashing detergent to the mix. You need to understand with simmering/boiling you still need to get dirty, you will need to pick and scrape the crap off to get it clean.(if you chose this method skip the next method and go to the degreasing step)
The method thats the simplest for the home taxidermist is called maceration. Simply get a bucket(5 gallon pail works good) stick your skull in it, cover the skull with clean water(no soap or anything else). Go to Walmart buy an aquarium heater the cheaper the better ($10-$20) stick it in the water, cover the top best you can with bubble wrap or anything else that will keep the heat in and not let the water evaporate. Set it all on a piece of styrafoam (sp?) wrap the outside in bubble wrap or some other insulator. You want to keep the water 80-100F. Let it sit. Make sure the water is still covering the skull completely every few days. Pull it out in 3 weeks, and check it. The flesh will melt away, no scraping no weakening no joints seperating. If its not done stick it back in, be patient. You may pour some water off and replace it with fresh to keep the smell down, but make sure you leave some, the bacteria is what eats the flesh off.(YES it will stink during this process)
Time to degrease. This is the most important step there is, and it is most often skipped. (this can be done inside, maybe a shop or unfinished basement)Take your skull and place it in a conatiner (I use tupperware) that allows the skull to be covered with water but not too much bigger. add clean water to the container until its covered, add your aquarium heater, a good clear detergent, and household ammonia. You can go straight ammonia, 50/50 or however much you decide. I use 1/2cup clear Dawn, 2.5 cups ammonia and the rest water. Cover the top best you can to prevent losing your water.
Walk away. The water will go cloudy as grease comes out, and you should change the water solution when it gets this way. (I usually change it every 1.5 weeks or so depending on species and grease content. If you simmered your skull it will take much longer than if you didnt) When your water stays clear for a couple weeks you should be okay. Every animal is different, I've done bears that took 2 months, deer that have been done in 3 weeks....everyone is different. Take it out, let it dry a few days look it over, grease spots will show if its not done yet.
Whitening:
To whiten I like to submerse(sp?) the entire skull in hydrogen peroxide, but you can get away with less if you make a paste with Hydrogen Peroxide and magnesium carbonate. You can use the dollar store kind which is 3% you can beauty supply 40vol which is 12%, you can use Pool shock which is 27% or the 35% you can get from a taxidermy supply place (make a paste, apply it up to the burrs and everywhere you want to be whitened.) Wrap it in plastic best you can and let it dry) when its dry there is a powder left all over the skull wash this off very well, let it dry(usually a few days), glue in any teeth or bones that have seperated or fallen off. You can seal it now with a matte clear coat, mod-podge, 50-50 emers glue/water or whatever, I usually wait to see if any grease spots turn up in a month or two, some dont seal them at all. If you buy lots of peroxide, I pour the peroxide in to almost the burrs, and place paper towel over the top of the skull up to the burrs, the peroxide will wick up the paper towel and whiten it up. For 3% I will let it soak for 2-3 days, any thing more 24-36 hours. Pull it out, rinse it very well, let it dry in the sun if possible. Glue your teeth or any lose joint. WEAR GLOVES WHEN USING PEROXIDE IT WILL BURN YOU, BLIND YOU, AND MAKE YOU UNHAPPY IN GENERAL!
*DONT use any soap, or cleaner or pool shock or anything else that contains bleach/chlorine. It will ruin your skull.
If I have missed anything and I am sure I have, feel free to drop me a PM. GOOD LUCK! let us know how it turns out.