Hooee! Well, first off, there's field dressing--"Gutting" the deer. Ya gotta do that before you think about skinning.
I've done the whole deal with just a large pocket knife, but it's easier if you have a 4" (roughly) hunting knife, a very sharp pen knife, and some heavy-bladed something to split the pelvis bone. (I have used a rock on the back of a knife blade.)
There are scent glands on the rear hocks. Some folks cut these off, cutting away a sizable flap of skin. I quit doing this, with the idea that it gets musk on the knife blade. I've never had a problem with musk getting onto the meat, so I quit worrying about it.
I--very carefully!--split the skin somewhere along the stomach, being cautious that I don't penetrate any "innards". I make a split all the way up the neck, and all the way back to the genitals. This is where it gets a bit tricky for the first-timer.
Separate the genitals from the crotch, but DON'T cut the urethra. Cut the muscle across the inside of the pelvis. Skin around the anus, cutting enough meat that it and the poop-duct is free from the hams. Then, CAREFULLY split the pelvis. You can then lift out the genitals, urethra, bladder and all that "bad stuff" and not get urine on the meat of the hams.
Turn the deer on its side; stuff starts falling out. Little cutting is needed; you can pull stuff loose with your hand. Cut the diaphragm. Split the breastbone and go on up into neck muscle. At some point near the head, cut the windpipe.
That's pretty much it. I hang my deer head up; I find it easier to skin them, that way.
So now you're ready to peel 'em and eat 'em, yea, verily like unto a shrimp!
It's easiest with two people; less fatigue on the "pulling" hand. That is, one person pulls on the skin, while the other carefully cuts against the hide. You just work round and round and down. Once past the shoulders, you can pull the hide down to the hindquarters just like pulling off a glove. (For that matter, you can pull the hide off with a vehicle and rope, once past the shoulders.) The most important thing is that your knife have a sharp blade, and hold its edge--or have spare knives.
The most tender part of the whole deer is the pair of muscles lying alongside the spine inside the body cavity. The tenderloin, or "Tenders". (If you ever help a "dude" butcher out a deer, tell him that these are "poison sacs", and you'll dispose of the carcass so they won't poison the dogs. He's gone? Can't see? Hokay! Cut 'em out, stash 'em in the fridge, and have yummies for later!
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Hope this helps,
Art