It's best to skin it almost immediately after it's been shot as that's the easiest time. If that's not possible you can hang the carcass for a few days as long as it's kept in a cool environment. Hanging venison is not always necessary like it is with other animals to tenderise the meat, though this can depend on the breed of deer. When I butcher roe I don't hang them at all.
To skin it, put a hook between the tendon and the bone of one of the back legs and hang it at a height that suits you. Using a very sharp, small knife, make an incision into the skin near the tendon, trying not to cut into any meat. You can do this on both the back legs, then using small movements use the tip of the knife to seperate the skin from the meat, using your other hand to pull the skin back. Don't make any cut where you can't see where you are going or you will cut into meat. If it's hung for a few days it can be a bit tricky to start, and some areas of the animal are more difficult than others, but once you get down to the main body you should be able to pull the skin down a fair way just using your hands. Use your common sense though and don't force it if it's not happening.
As for the butchering, it depends on what you want to do cooking-wise. You'll want a nice large work surface with lots of room to move. Your small sharp knife, a larger one, a saw, and if you've got one, a cleavor. I start by taking off the legs. Put the carcus on its belly so you can see the top of the spine. Try and have a good look at the muscles. To take the legs off, you want to look at where the largest muscle from the leg ends, and also where the loin (the meat running either side of the spine) ends. You need to make a call that includes as much of the leg muscles as you can, while losing as little of the loin. Once you've made your decision. Use your knife to draw a straight line across the back, then continue that line right down either side. Make sure the line has cut through all the muscle right to the bone, then use the saw to go through the bone (never cut through meat using the saw, it's only for bone). Once you have the legs removed together, you can seperate them by sawing down the middle (from underneath). Next, I carefully remove the loins. This is the best meat on the animal and I remove the whole muscle, going right up to the neck.
Next, remove the shoulders. Belly side up, count the 5th or 6th rib up from the neck and make an incision through that you can see from the other side. Whether it is the 5th or 6th rib depends on the breed, but you want to be pretty much clearing the shoulderblade, so have a look from the top, and if the 5th looks too close to the front leg, go for the 6th. Once you have the incision through, turn the carcass over so that the spine is facing you again and, using the incision as a guide, cut another line straight across the bottom of the shoulders, and again continue the line down the belly so you've drawn your line straight across the top of the animal, then use your saw to finish.
Cut the bones down for stock and that's basically it. You shouldn't need any help skinning, but it's good to have help butchering if you can. Sometimes it makes all the difference when you're sawing to have that extra pair of hands.
As for cooking, the meat on the shoulder and anything that looks useable over the ribs is great for stews and sausages. Of course you know how lean venison is, so if you're making either of those things be sure to add plenty of pork belly or belly bacon, and always lard or bard legs when roasting. Rather than roasting a whole leg I often seperate each individual muscle from the leg, remove the sinew and sear and roast them. It works beautifully, but is a little fiddly if you haven't done it before. And next time, try and get your man to save the liver. Fresh liver, a little flour, plenty of sage, some salt and pepper and a quick toss on a seriously hot pan? Yum.
Good luck, hope all goes well.