I've had good results following the instructions from this old Field and Stream article by Keith Mcaferty...
Tanning a deer hide is a rite of passage, cementing blood ties to our hunting forebears who depended upon skins for warmth and who respected slain animals by never letting any part go to waste. Using an alum solution (you can find ammonia alum at pharmacies) departs from tradition—ancestral hunters used brains for tanning—but will render your hide soft and supple. The reward is a memento that serves a dual purpose as a beautiful wall hanging or a comforter for a winter night. —KEITH MCCAFFERTY
STEP ONE Skin the deer and bone out the tail. Scrape every particle of fat and flesh from the hide with a knife. Begin the tanning process or preserve it with a generous layer of non-iodized salt. Salted hides can be air dried until the onset of warm weather, or frozen.
STEP TWO Soak the skin in water in a plastic garbage can until it softens, changing the water often. Drain, then pull the skin back and forth across the edge of a board. Scrape it with the back edge of a knife or an old hacksaw blade with dull teeth. Do not expose the hair roots.
STEP THREE Dissolve 2 ½ pounds of salt in 4 gallons of water in the garbage can. In a plastic bucket, dissolve 1 pound of ammonia alum in a gallon of water. Slowly pour the alum solution into the garbage can, mixing thoroughly. Soak the skin for four days, occasionally stirring to make sure the hide is well coated. Rinse thoroughly with running water.
STEP FOUR Tack the hide, hair side down, to a piece of plywood. Partially dry it in a sunless place, then rub in a coat of fat liquor oil (3 ½ ounces of neat's-foot oil combined with 3 ½ ounces of warm water and 1 ounce of ammonia). Work in half of this mixture, allow it to stand for an hour, then repeat. Cover with plastic overnight.
STEP FIVE Remove the tacks, dampen the hide with a wet cloth, stretch it, then rub it back and forth over a sawhorse. Redampen it and repeat, applying additional fat liquor sparingly. When the hide is perfectly supple, smooth the surface by chafing it with fine-grit sandpaper.
You can purchased the ammonia alum from Van Dykes supply... 5 lbs is like $15. This is a buck my son killed last year which now graces the couch in my office...