Squirrels are quick and easy. Make a cut from nuts to neck (skin only), turn squirrel inside out, take your mouse hawk (small version of a tomahawk...a small hatchet could work) and cut off their feet, tail, head. Then you can cut from the neck to the tail end and open squirrel. Clean out and prepare how you like it.
I like squirrels mixed with red beans and rice. First I cook the squirrel on a fry pan until it is near done. Cut the meat from the little wire bones and mix in a pot with red beans and rice. Since I am a fan of garlic I usually add in a couple cloves. Add in a small can of diced stewed tomatoes and simmer for another .5hr.
Deer, I got a butt out tool for my birthday last year so my new way is to start with that tool.
After that make a cut from the crotch to the sternum. Pull innards out and cut the diaphram (if the bullet did not do the job for you) and pull out the lungs and heart. Dont forget to cut the trachea. If you are using a larger knife, be careful when you get two hands in there. A buddy of mine uses trauma shears to cut the trach.
Make sure you get all of the insides out for the coyotes and get the deer to your vehicle. Now, I know there are a lot of opinions on how to avoid "gamey" meat. My personal findings have let me to beleive it is in how you take it out of the woods. Try to avoid dragging where you bounce the deer around. Each hit is breaking cappilaries and causing blood to enter the meat instead of draining (which is why you let the deer hang for a day or two before processing).
Each person processes their take differently (like any butcher). I generally keep it simple. Start at the top and work my way down. This allows me to be maticulous about the cuts and minimize waste.
I cut out the usuals, roasts, steaks, burger meat, stew meat, kabob meat, spiedie meat (local fare consisting of cubed meat marinated in an italian dressing based marinade for 24+ hours put on skewers and grilled on open flame), The hide gets caped and removed to be placed in a brining solution for pre prep for tanning, finally the carcass goes to the revine of death. A place in the back of the property we toss the carcass of our kill for the coyotes and so nobody has to smell it.
My favorite way to prepare venison is on a cast iron skillet with Promise (heart healthy), steaks cut up thin and about the size of a dollar, red onions and yellow peppers. Toss on some leeks and you got some gooooood vittles.
For a roast I prefer to use a dutch oven but I usually end up using a regular oven for convinience. I like to do it two ways, first is to put a dry rub on it and cook in the oven uncovered. The other way is to put beef stock in a baking dish, put in the roast, boiling onions, potatoes, celery, carrots, and shredded cabbage. Cook meat first...when there is about 1 hour left in cooking meat...add the veggies. Cook unitl done and serve. Goes great with an IPA beer like Dogfish Head.
I then take the lesser quality meats and put them in my very own marinade. Let them soak for at least 1 week. I then get a nice smokey fire going. Hickory is what is plentiful around here so I use that a LOT. I also use apple and sugar maple. I then prepare my smoke box and racks. When done it is about 8' high and 4 feet accross. I have a trapdoor at the bottom to add wood and soaked skins for extra smoke. Let meat dry over 12-18 hours and package. For long term storage I vaccuum seal it, for near term use, I bag it.
I could go on but I will spare you.