First,trim the bulk of the meat off.If you have a place where you can let it spoil a few days without causing a divorce,put it in a garbage bag and let it sit at least three days.This will loosen the meat up and reduce cooking time.
Don't boil,just simmer.Put a handful of baking soda in the water and a squirt of dishwashing liquid.
After an hour or two,pull it out and check progress,picking off any meat and tissue you can.Keep repeating this process.If the water gets real dirty halfway through,change for fresh,adding more baking soda and soap.
You can scramble the brains with a wire or screwdriver and shake those out after a couple ours of simmering.I usually blast them out with a garden hose.Don't stand directly behind the brain cavity hole!
When the stuff gets loose enough,I use the garden hose to flush out the sinus cavities,using gentle pressure.Work over an area that is clean enough that if small teeth etc,fall out,you won't lose them.I have an outdoor table made for this using 1/8" hardware cloth on the top.
There are some spots on the rear of the skull where neck muscles attach and these spots are tough and you will have to do some scraping with the end of your pocket knife.
Once it is cleaned,it may or may not need degreasing.There will be a grease ring on the base of the antlers most likely.Clean that off with the dishwashing liquid and a small brush.
Let the skull dry to see if you have any grease spots.If you do,they will look like wet spots.Some deer will be fine,same with antelope.I submerge mine in acetone but that can be spendy and it is a flammable liquid,so only outside and no sparks-even static.
Degreasing often takes days,sometimes weeks.You are just diluting the grease and waiting for it to leach out on it's own,so it won' go fast.Some use dishwashing liquid in water and it may work on mild grease,definitely is safer,but the acetone has always worked better for me.
Bleach only after removing any grease spots.I use beauty salon type bleach.You can get it from Van Dykes Taxidermy Supply or a salon.Some submerge skulls in household peroxide and say that works.If you use the salon stuff that you whip up like shaving cream,brush it on and wrap the skull with cling wrap to keep it wet.Sit it in the sun if you can.Wash the stuff off next day.
The best thing I have found to seal the finished skull with is Future floor finish,thinned 50/50 with water.If you want a lot of shine,don't thin it.It is crystal clear and non yellowing.The thinned version can be wiped on the antlers too and really brings out the colors.If the antlers get too much sheen,just wipe them down with a rag and Windex.Just brush the Future on with a clean brush.
After sealing,I glue any loose teeth or nasal bones with white glue.After sealing because the Future can soften the white glue.
Hang it on the wall.