My grandfather hung them upside down. Then he quickly snapped the head down and back to break the neck after which he used a knife to slice the throat. He had a trick to take of the skin, but I don't remember how he did it. IIRC, the rabbit needs to hang for at least a day before you consume (never eat it the same day it was killed, has something to do with taste, I think).
My father tied the rabbit up. He had a friend who used a big knife to cut off the head in one blow, but I guess you need to practice a bit to be able to finish it with one clean blow (so yeah, your first few times will be a bit messy). After the head is off, you hang it upside down (put a bucket under it) for a day.
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