I'm no expert on the subject, just want to share what I've learned and encourage others to try it-safely. There's no way I can cover it in detail here, just want to encourage folks to think about the DIY possibilities.
First step is preparation. I take a 100 qt Igloo on most hunts here in TX, the weather and geography make that part of a good plan. A 54 qt will hold one S TX deer, my 100 qt cooler will hold two (or a big hog!) easily. Inside I'll put at least 4 bags of ice at my last fuel stop. Next step comes after the critter is dressed and cooled a bit, if possible. Skinning is pretty straightforward, many good videos on the subject on youtube. Quartering pretty straightforward as well, with S. TX whitetail the leg quarters, loin, tenderloin, heart and liver go in the ice chest and get covered with ice. Takes no more equipment than proper field dressing! I generally trim all the good meat off the ribcage and discard it or use it for coyote bait. Keep the meat covered in ice until you get home, draining off water and adding ice as needed.
Converting your kitchen to a butcher shop is no big deal, a good scrubbing before and after are important steps that can't be overlooked. Efficient butchering involves sharp knives, cold meat, and a good cutting board or two. I keep the meat in the cooler until it goes on the cutting board. I generally just debone the meat and package it as roasts or 1" chunks. Chunks are used for stew or sausage. I like to package the meat in vacuum or ziploc freezer bags, labeling is important. I try to spread the bags of meat around in the freezer so they freeze quickly. Once everything is in the freezer you can scrub the kitchen and start planning menus!
I've only hit the high points here, please share your tips or feel free to ask questions! Nothing against commercial processors but they aren't always the best way to get wild game into the freezer.