i do alot of work with my taxidermist, and i'm sold that his method is the easiest way to do skulls and bones (aside from beatles of course...but you don't really want those getting out in your fur shed).....take the skull/bone and put it in a bucket of water...if it's warm outside put it outside preferrably out of sunlight..the warmer the better...leave it alone for a couple weeks...the bacteria in the water will break all the meat down and make it fall off...only down side is that once you disturb the bucket and break the film on top, it's quite a nasty smell...if any meat is left, just save a little of your old water, put new water in and let it sit another week or so....once all that is gone....just like dirtchipper said....let it sit in peroxide for a week or so...it bleaches it out really well and doesn't weaken the bone
only the large chunks of meat will fall off..... you still have to have a water pick or an pressure washer to get the rest of it off.... then comes the hydrogen peroxide part. letting it sit in regular hydrogen perxide is a waste of time. go to the store and by a hair frosting kit and get the process over with and you have a much nicer finaly product than regular H30.
The process described by akitzman is called maceration. I clean a lot of skulls of several different species and that is the process of choice for me. And if you use this process anytime other than the during the heat of the summer, Kris Meyers is correct that some meat/fat may remain. I use the process year round but I use an inexpensive submersible aquarium heater to keep the water at around 90 degrees F. To do a properly prepared whitetail skull, it takes about 7 to 10 days to get the soft tissue off. It does stink though.
But once the soft tissue is gone, the skull or bones is NOT ready for peroxide. Bone contains grease and that grease needs to be removed. If you go straight to peroxide, it will oxidize the surface and will look pretty good but over time, the grease in the bone will migrate to the surface and make if yellow again. Depending on the specie, I degrease in warm water (120 F) and Dawn dish washing liquid for days, weeks or months before moving on to the peroxide soak. If the bone is degreased thoroughly, they will say white.
It really depends on what you plan to use them for as to how white you want them to stay. I clean peoples' trophies and I want them to look as good 5 years down the road as they do the day they pick them up.