Funny you should ask. A couple hours ago I just finished cleaning up butchering one myself. You get more meat and it's done by you--pride of ownership. Okay, if this is a trophy buck that you're having mounted, then hang it by the legs with gambrel. You'd have to start skinning at the legs, and take it down to the neck--don't cut the hide at the neck; let your taxidermist do that. Otherwise, do what I do and hang by the neck. Either way, remember to lay some plastic sheeting, garbage bags or a cheap tarp underneath so you don't screw up your garage floor.
Hanging from the neck, cut the hide all the way around at the neck. Cut the hide down the front (from the neck down to where you field dressed it). Then just grab where you cut at the neck and pull like hell.
Side note: If you're allergic to pets, you may well find you're allergic to deer fur--I found I am, so I wear a dust mask for this.
Now you may find it easier to make some hide cuts at the shoulders and hind quarters once you get there--I certainly do, but then I don't save the hide. That said, you only need get the hide past the knees. Then use a sawsall (or hacksaw, but I like my cordless sawsall) and cut at the knees.
After that hair generating process, many people stuggle with every piece of cut venison, trying rinse all the hair off after butchering. Don't do that. Instead, use a propane torch and singe all the hair that got stuck to you now skinned carcass. When you do this, don't cook the meat. Just pass over the hairs briefly and singe all the hairs stuck to the carcass. Go ahead and laugh, but I've never had anyone find hair in my venison yet, and it that takes 30 seconds as opposed to up to an hour under a faucet. By the way, I find it's also a good idea to singe (not burn!) the hairs on the neck fur still attached--you don't want any more falling off.
Now you're ready to cut up the meat. A sawsall with a metal cutting blade is most helpfull for cutting bone. I use my regular kitchen knives for the actual butcher. Use a sharpening stone to get them razor sharp before you begin. You'll thank yourself for the upfront effort in time saved and safety gained during the butcher. If I were to only have two knives for this, I'd pick a boning knife (similar to filet but shorter) and a carving knife. Look at an older cook book and it will likely show you what sections of beef go to what cuts. That's a good starting point because it somewhat applies to deer or most anything else you butcher. Grab a hind quarter and cut the muscles into the joint. Now grab the leg of that quarter and rotate toward the deer's head to dislocate it. Once done, cut the connective tissue in the joint, while holding the leg firmly--it'll have more weight than expected and you don't want to drop it. There are roasts and steaks in this. Cut your steaks against the meat grain, and cut your roasts with the meat grain. Basically one muscle trimmed (and cut to preferable size and/or weight) is a roast. Take those same muscles and cut across the meat grain to desired thickness for steaks. Trim all fat off--it's not beef fat, this stuff is nasty when cooked and doesn't come off plates or pans in a dishwasher.
Next make two cuts, one on each side of the spine. Grab the muscles you just cut and feel for a separation between the ribs and the muscle. Cut along that muscle. These are your backstraps (best part and very tender). Roast or grill as is, marinated or seasoned if you like. Beneath the backstraps are your rump roasts. Don't forgot to harvest them as well.
Grab the front legs and separate them. Cut into the separation between each leg and the ribs. Cut around the shoulder too. Grib the leg firmly as it will fall in your hand. There's no joint to separate here. Depending on deer size, you've got roasts, steaks and/or grinder meat.
Okay, those (other than the tenderloins, which you probably destroyed dragging it home
) are the best parts. Also, I've never tried, but I knew some old guys who liked to save the heart, stuff it and roast it. They said it was good eats but your results may vary there. Anyway, I hope you remembered to save the liver when you field dressed it. You might have some roasts in the neck, but it's more likely grinder meat. Pick the bones as clean as you can with a knife and use whatever other meat you get to grind. Do not, NOT, leave much fat on your meat. It's not normal fat. Don't try to cut the rib bones and make bbq ribs either--I've tried that, and because of the fat, it's !@#$#@$ disgusting. So trim fat off of whatever is left and grind it.
Happy Butchering.