I've got a bear skull that has been outside for about a year. Looks like all the tissue is gone, but it looks all groady where it was laying in the dirt. I want to hang it in the house so I want to clean and sanitise it. How should I do that to not destroy it? Also how should I affix the teeth? Some were falling out of the lower jaw. Would clear silicone be ok?
I read in another thread about sealing it. What do you use for that?

This doesn't really help now, but next time boil it for a few hours then power wash everything off.  

That's how I do my deer.

Personally, I only have done soaking in warm water for a period of time.  Beetles would be my next suggestion.

Bascially, how I have done mine is using an aquarium heater turned up all the way in a 5 gallon bucket with the skull.  It's best to have as much meat, brains and eyes out as possible as it just slows it down.  Lid is essential to keep the stink down and to stop maggots/evaporation.  I warn you, this smell will be absolutely horrible.  It soaks through latex gloves, but not nitrile.  I would leave them in this for about a month.  The heat also helps loosen grease in the bone so it speeds up the degreasing.

After it is all clean, it goes into another bucket with heavy amounts of Dawn dish soap (great degreaser!) and ammonia.  Together, they really help get the grease out of the bone.  Yellow bones are due to grease trapped inside.  Bears are a very greasy skull so it may take a few months to get it looking good.  The hogs that I have done, I even drilled tiny pin holes on undersides of areas that were a high concentration of grease.  It allowed the soap and ammonia to get at it better.  It would take me many times of drying to check for grease then re submerging to degrease even further.

Once done, submerge the skull in Hydrogen Peroxide for a day or two (if using the cheap stuff from the medical isle). The teeth will all come out and can be glued back in with Elmer's Glue once complete.  Then seal with a non yellowing clear coat from an aerosol.

Sorry if this was long winded, but it urks me to see a trophy skull all yellowish and nasty!

Bear skulls are very greasy.  Let it simmer for a few hours in a solution of dawn dishwashing soap and water (don't overdue the dawn).  Then I would let it simmer in just water for an hour or so.  Let it dry and then re-attach the teeth ( I use a little bit of gorilla glue epoxy on the back side so no one can see it.)  If you want to whiten it use some Maximum Lift 40 Developer Crème.  Paint it on as much of the skull as possible, wrap it up in saran wrap then stick it near/on a heat source for several hours or overnight (like a wood stove).  Make sure it isn't so close that the plastic wrap melts.  After that rinse it off very good in warm water.  Make sure you wear some gloves as the 40 solution is fairly potent.  I am not a professional but you should get good results.  To seal it after it dries use Paraloid B-72.  Here is some good info on the application.  http://www.taxidermy.net/forum/index.php/topic,2213.0.html