To kill them, I'd grab their hind legs and their heads, stretch them out, bend their heads back to stun them, then break their necks by whacking them with a hammer handle. After killing them, I'd hang them up with a hook between bone and tendon in a back leg. Unfortunately I didn't always get a clean kill. Several times I had rabbits that revived while I was hanging them up. They'd shriek and kick in a way that would rip you open if you got too close. The shrieking was really unnerving. After all, I didn't want to hurt them. I just wanted to kill them. I'd have to grab both hind legs and whack them again with the hammer handle. After they were definitely dead, I cut off their heads, let them bleed out, then skinned them. I can't imagine anyone managing to skin a living animal. I just don't see it as possible.
Now as I read your post, in comfort, with my pet rabbits running about...somewhere along the way I lost the ability so to speak to sense the line between food & friends.
I am probably not alone in this these days.