Meek.... "Buzzards gotta eat; same as worms." - Josey Wales
To answer the question in some detail, "what do you do after you shoot an animal?":
Varmints: Make sure they're dead (not suffering), then leave 'em.
Game:
First, let them go die (in the case of large game). Wait a good half an hour before tracking if you have made an excellent shot. Wait an hour or 2 if you think you hit them with a bad shot. Tracking itself can be an adventure and is a whole nuther subject unto itself - and very unfortunately, will occasionally be unsuccessful, sooner or later (knock on wood). A second shot is sometimes required also, if you can see the animal is down, but not dead.
Second. Gut them immediately or almost. Regardless of the game: fish, bird, or mammal, they got guts that need to be taken out. Cut from [color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color][color=#FF0000]█[/color] to sternum, reach in and pull em out - may require some cutting around the insides of the rib cage. Then, in the case of organs that you want to save & eat (such as deer heart or turkey liver or whatever), place organs in a plastic bag; place on ice. Any number of carnivorves and omnivores will greatly appreciate your gut pile - coyotes, wolves, bears, buzzards/hawks/eagles/falcons/kites, crows, racoons, skunks, etc. I think owls eat only live prey, not carrion, but these others will eat it, 'cept maybe falcons & kites eat only live as well - not sure. Possums might even eat the guts - not sure.
Third: Get the game out of the woods & back to camp or home (may require a horse, tractor, 4-wheeler, wheeled carriage, 3 or 4 of your buddies; whatever). May require some in-field partial butchering to make the carcass into a manageable/packable size (esp. elk and up sized).
Fourth: Skin & Butcher 'em; requires a good sharp knife....in cold weather, you can let a deer hang a few days to make the meat tenderer or tastier, but in slightly warm weather all game must be butchered soon (within 3-10 hours let's say), and in very warm or hot weather, immediately. Carve out the meat, wash off, place into plastic bags or other container, put on ice. Butchering specifics depend on species, and is a skill that you get better and faster at over time, but the basics are the same, regardless of species - carve the meat away from the bones, and get the parts small enough to fit in the ice chest. Take skin and discard or save & have tanned (or tan it yourself if you know how and are so inclined). During the skinning process, you cut off and save whatever trophy you want, if applicable - a deer or elk antlers or head, a turkey beard, pheasant tail, whatever. Discard carcass (makes a good crow lure.
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Fifth: For large game, you *may* want to take some or all of the meat to a professional meat processor, and pay the man to have it turned into sausage, hamburger, steaks, or just whatever, with possibly spices and/or suet added esp. in the case of hamburger or sausage. Or you can do this stuff yourself with grinder, sausage maker, etc.
Sixth: When I get home, wash the meat off again, and place into freezer bags or freezer paper or whatever (this step is already done for meat you had processed - just place in freezer). Additional butchering may be done to make into smaller meal-sized pieces for freezing, since it's so hard to cut into smaller pieces after its frozen.
Seventh: As desired, thaw, consult wild game cookbook, fire up the grill, frying pan, oven, or smoker, and enjoy! "Where's my Hasenpfeffer?!?"