It's good to see you're thoughtful enough to ask these questions before you harvest an animal. Thank you for that!
As trappers we skin, put-up & dry so we can sell the pelt, not all hunters do for reasons of their own. In fact, most hunters in my area do not process any of the canines they shoot. I'd suggest if you're hunting them be cognizant of bullet damage and the amount depending on which bullet you use IF
you plan on selling the pelt.
I had a "friend" who thought a grey fox was going to escape my trap so he shot it with a .223. I spent a little over an hour sewing the pelt back together. It looked like Frankenstein Fox but I did get $30+ for it when top that year was in the low-$50's.
I'd suggest several directions for info if you want to skin and sell. There is of course plenty of info to be found on different trapping forums by using the "search". Some of what you find will contain pics of the steps during the process and pics are worth 1000 words when it comes to skinning. There are also some pretty informative books and videos out that are a very good help as well for processing fur.