Depends on if you want the hide. You can skin like a furbearer (raccoon, muskrat, mink) and cut across the insides of the rear legs and then pull all down to the head, you end up with a 'mitten-like' skin that you can stretch, inside out. If you don't want the hide the easy way is to cut the skin all around at the midline and pull skin both ways, left hand to the head and right hand to the tail. The best advice for a hard skinning anything is to do it as soon as it's down before it gets cold. Anything cold is tougher to skin. Any coyote is a real tough skinning job.
I cut around the middle and pull both ways. Just gut it AFTER you skin it!!!! Get the scent nodules out under each
arm pit or you won't be eating it! Stinks when you cook it. I also boil em in vinegar water until it stops "foaming" up the water. Gets a lot of the gameyness out of it. Good eating if they ain't old critters. Also remove every trace
of fat on the carcass.