It's not a fun job, but it has to be done - field dressing a deer isn't pretty. But the freshness of your meat depends on quick butchering of your kill, and it'll cut down on how much weight you have to drag back to your camp. Besides, if you're going to kill and eat an animal, you should be able to break it down, too.
It doesn't take a lot of time to field dress a deer - about 10 minutes, once you know what you're doing - but it does take a strong stomach and a very sharp knife. Before you do anything else, if you're hunting in an area that requites tags, immediately tag your deer before dressing it. The tag has to remain with the deer at all times, otherwise you could be fined a hefty fee and have your deer confiscated.
First, carefully cut a circle around the anus so it can be removed from the inside of the animal - if you want to be extra careful, you can tie it off with a string to avoid contamination of your meat later. If it's a buck, remove and discard the testicles, and cut a circle around the penis so it can be removed from the inside, in the same fashion as the anus.
Starting near the pelvis, cut open the stomach cavity to the ribcage. As you cut, feel your way along with the first two fingers of your other hand - very carefully, as you don;t want to cut yourself. Your goal is to cut only through the skin and a thin layer of meat, and to not cut through the entrails. Now cut through the ribs and skin, following the breastbone, up to the neck (this is a much easier cut than it sounds if you have a sharp knife - but don't twist it, as you might break your blade) and continue cutting on up to the base of the skull.
Cut the diaphragm free - the thing sheet of muscle separating the stomach area from the chest cavity. Let gravity help you roll the deer to its side, then gently nudge the organs out of the body cavity. You may have to tug a little, but they should come out fairly easily. Just be very, very careful handling the bladder - you'll need to reach up into the pelvis and pinch it shut while you cut it free. If urine leaks onto the meat, clean it off with a little clean water. Clean out any debris remaining in the cavity, including any stomach contents or other substances. Set the heart and liver aside, preferably in a cloth bag, if you or a friend use them.
Then clean yourself off, take a short rest, and haul your prize back to camp. It's not the most pleasant part of hunting, but a necessary skill - knowing how to field dress a deer will save you having to carry as much weight and ensure that your meat stays fresh.