Congratulations on taking your son to hunter safety. I have three sons and went through the class three times. Each time I learned something new or met a new friend or two no five...lots of new friends. I don't remember them going into the "field dressing" that deeply, although it's been years since the classes.
Here are a few tips I learned along the way (been hunting since the 50's). I am no expert, and others may have better ways to do it.
There are some items you should have after the shot. I always have a small spray bottle of peroxide. Nature has a sense of humor and ads "red" to leaves and twigs. When in doubt about it being blood, a little spray of peroxide will let you know. If it is blood it foams up, if not, nothing. Also after field dressing it is great to clean your hands with, killing germs and removing blood.
Have a sharp knife. I use the lansky knife system and then buff the blade with a bench style buffer. (yes the buffer will snatch the knife and wing it so be careful.) But when done properly I can shave a piece of 8 pound mono 6-7 times with no effort. This also means you need a first aid kit when afield.
Rubber gloves like many mechanics wear. Harbor Freight has a purple glove that is really strong. Some worry about disease from the blood, I just find it easier to clean my hands. (There is a good chance mosquitos are around and having bloody hands and clothes turn them on.)
Remember to use bug juice. Deer are loaded with ticks and when the deer die, they look for a new home. I drug a deer 10 yards by one leg and had 50 ticks going up my arm.
Always have a good flashlight or head light and a good rope.
First, make sure the deer is dead. Seriously, to field dress the deer you have to get near it's hooves and if you don't know, they can kick like a mule and are as fast as a rattlesnake when they kick.
Drag the deer to a bit of an opening and roll it on its back. If you are alone, it sometimes helps to tie one back leg to a tree to keep the legs spread proper. Taking the knife, make a small slit, not deep, at the center of the belly just below the rib cage. Some gas may escape then. When I say gas I mean noxious foul fumes.
Place two fingers of one hand in the slit and pull the skin on the belly up and away from the bowels. Insert the knife and make an incision down to the rectum making sure not to cut the intestines. If it is a buck, cut the skin around the privates and locate the urine tube. Trim the skin around that until it to the rectum. Don't cut the tube, just let it lay. Now place one hand inside the stomach cavity and pull the intestines out of the deer. You will find connecting tissue by the spine, cut the intestines clear, all the while trying not to cut open the stomach or intestines. They contain very foul smelling stuff. With the intestines pulled out, you now have one section leading to the anus and the other leading into the chest cavity.
Cut around the anus and pull the intestine out, some fecal matter will probably drop. Insert the knife into the anus track and trim the intestine away from anal track (cut all the way around it, but don’t cut the urinary tube or intestine). Once it pulls clear, and this is the urinary track also, they will pull out a few inches. The bladder will also be pulled toward the anal cavity. Now reach back into the stomach and remove the intestine and bladder and privates. The bladder will most likely be partially full, some like to carry a bottle to harvest this for future hunting trips. I leave it with the pile.
Next go into the cavity and cut the tissue that separates the lungs from the stomach by trimming around the inside of the ribs. Some like to cut up through the chest plate to make the next part easier. Then reach up to the base of the neck inside the chest cavity. You will find the tracheal tube coming from the neck. Cut the tube as close as you can to the neck and pull out the lungs liver and heart. This is normally where someone cuts their finger rather badly. Many people keep the heart. It is delicious in chili or with onions fried.
Now drag the deer away from the gut pile and lay it on its stomach to drain.
You've field dressed a deer. If you are hunting a public area where bird watchers and joggers travel, you may want to cover the gut pile with some leaves. Never leave any paper towels, rubber gloves, or anything on the ground.
Now Tag it, and drag it out. Many old times will take the front legs of a buck and wedge them into the antlers, then tie around the legs and neck and drag that way. Always drag from the front of the animal, it's easier.
When you get home, find a stick and wedge it into the chest to keep it open, take some napkins and clean off the blood in the cavity and hang the deer off the ground. I prefer to hang them head side up to let the rest of the fluids leave the body and not pool by the neck. If it is warm, pack ice bags in the cavity.
Take pictures and post them on the forum..
Good luck
Fred