My process is as this:

• Skinning
  Skin out your skull the best you can. Remove the eyes, cut off as much meat as possible and remove the jaw. After the first skinning and scraping, the skull still will look like there is a ton of connective tissue and fat covering the surface along with muscle and brain hidden within the cavities of the skull.
• Boil
  To loosen the remaining tissue, boil the skull for a good 30 minutes in plain water. This will break down fats, loosen the grip of tissue on the skull and make for an easier second scraping once the skull is cool enough to handle.
• Pressure Washing
  After a second scraping, take a pressure washer to it and blow it into all the crevices, into the base of the skull where the brain is, into the nose cavity and nasal cavities.. Run the pressure washer over the skull until nothing else will come loose (if you don’t have a pressure washer, a car wash works great, just do it during low car was hours).
• Second Scraping
  After the pressure washer, pull off the newly loosened flesh, muscle, tissue etc with a knife or pliers. Now let it dry out for a day or two in a secure place so the neighborhood dogs don’t run off with it.
  I hang mine on a chain out of reach from scavengers.
• Third Scraping 
  After the skull dries out. Scrap, poke and pull everything you can out of the brain cavity, sinuses, ear canals (which you will need to break away). This may take a few sessions of work. I take rigid wire like a clothes hanger and make small hooks I can slip into cavities and pull out tissue and material from all the tight places.