From Alaska Fish and Game:
"The initial step in cleaning a skull is boiling. The hair and hide should be removed. They contain oils that permeate the bone when boiled and the result is a yellow, greasy skull.
If the skull cannot be cleaned soon after the animal's death, freeze it. Rotting skulls are no fun to clean and may cause a revolt in the household. If the skull is malodorous from decay, it will be repugnant during boiling. In this situation, boil it on a camp stove outside, or in the garage, in a castaway pot.
Immerse the skull in water and let simmer. A thawed wolf or bear skull requires 2.0 to 3.0 hours of simmering. Smaller skulls, such as marten, fox or lynx, take about 40 to 60 minutes. Frozen skulls will take about 15 to 30 minutes longer. The skull is ready to be cleaned when the muscle pulls off easily. Do not boil the skull too long as this can crack the teeth and soften the bone. It is best to remove the meat and brain tissue while they are still quite warm. Once cooled and dry, thorough removal of tissue is more difficult.
The muscle, if cooked sufficiently, comes off in hunks. Use a small knife. Nerve and connective tissue can be teased out of holes and crevices with a wire or large tweezers. The tough part is cleaning inside the cranium (brain case). This is done through the oval opening at the back of the skull, where the skull attaches to the spine. Repeated rinsing flushes out loose tissue.
After the skull is as clean as you can get it, soak it in an enzyme-bleach powder (such as Biz) using about ? cup to a gallon of water. Don't use liquid bleach, it is harsher to the bone and does not have the enzyme action that is needed to break down residual tissue. Leave big skulls (bear, wolf, caribou, bison) in this solution for 3 days. Smaller skulls may require less than 1 ? days. The skull has soaked long enough when the remaining tissue can be easily removed.
A small, stiff-bristled brush, a small knife (scalpel) and tweezers are adequate tools for doing the final clean up. Rinse the skull well after you have removed the last, stubborn tissues.
Teeth will invariably loosen during boiling and cleaning. Hang on to them and glue them back in place with white glue once the skull is clean and dry."