NorthernCaliforniaHunter's instructions are good.The only thing I would add,is that bears and some other animals need degreased after all meat and tissues are removed.This has to be done regardless of the method used.
All bugs do is remove meat.The skulls are very funky when the bugs are done with them.They still need to be soaked in a solvent for quite awhile until all grease is gone.
When a skull has been cleaned,after drying-say,overnight,if you see what looks like wet or waxy spots,that is grease.Young bears have less,older bears have more.I soak skulls in a sealed bucket of acetone,kept in a steel shed outside.
Degreasing is a slow process.Think about it.The porous bone is saturated with grease which has to be diluted by the sovent till it gradually leaches out on it's own.This may take a week or it may take a month.
Just submerge in the solvent and check it in a week.Leave it out till you think all solvent has evaporated from the skull.If you still see wet/waxy spots-back in and repeat.
I have heard of people useing Dawn dishwashing liquid and water but it has never worked for me on a truly greasy skull.I couldn't possibly live long enough.
After complete degreasing,the skull can then be bleached.After that,it should be sealed.The best thing I have found for that is Future floor finish,thinned 50/50 with water.It is crystal clear,soaks in to every pore and cleans up with water.When thinned like this with water,it is not shiny but gives it a smooth,eggshell like feel and protects it from getting dirty.Poly will yellow some over time.
As I said,the instructions above are good.I simmer in baking soda but basically the same.
1.Remove all meat
2.Degrease
3.Bleach
4.Seal
Regardless of the flesh removal method,these are the basic steps for all.
Done right,a simmered skull can look as clean and pristine as a bug cleaned skull.Keep in mind that tiny teeth like premolars and incisors of predators become loose fairly quickly so don't pour off any cooking water without straining it well.It is easy to lose these teeth.Any time you remove the skull from the water to pick flesh,it is a good idea to do it over an old window screen to catch any small teeth that drop.As teeth loosen,put them in a cup or jar and reinstall them later.
I should add also,I normally,after manually trimming the bulk of the meat from the skull and before simmering,I put it in a black garbage back to not let it dry but let it spoil for a few days or longer if you can stand it.This drastically cuts simmer time.Cook it to hot and the flesh firms up and takes much more time-exposing the skull to heat,longer than necessary.
Married guys,proceed at your own risk.Apartment dwellers-pay a taxidermist.
A garden hose on very low pressure can be used to gently flush brain and sinus cavities.Go very easy with the fine sinus bones.
Lastly,use rubber gloves when handling,clean and disinfect hands after any contact.Bears carry stuff.