The first thing you want to do, after catching a wild rabbit, is to calm the rabbit down. A panicked rabbit does not make for a pleasurable dining experience. It taints it. Pet the rabbit. Maybe say something soothing, like "Easy, Brownie, easy" (if the rabbit is brown) or "Easy, Gray Boy, easy" (if the rabbit is gray). You might just say, "Easy, little bunny." (But, really, can't you come up with some kind of name besides "bunny"?)
Feel the belly. It should be plump and fuzzy. But skinny is fine, too. Feel the ears. They should be soft and pink. MAN, I LOVE THE EARS.
If you like your rabbit spicy, try rubbing him with wild sage or wild mint.
Place the rabbit on a rock with good drainage. Next, take out a long, sharp butcher knife. Try not to let the rabbit see the knife. You may not want to look at the knife yourself, as some of them are kind of scary-looking.
Hold the rabbit down firmly with one hand. With the other hand, take a carrot out of your backpack. Still holding the rabbit, place the carrot on the rock and slice it with the butcher knife. Then feed the carrot pieces to the rabbit. If the rabbit doesn't eat all the pieces, feel free to eat the leftovers.
Let the rabbit go. For fun, throw the knife at a tree trunk, to see if you can make it stick, like Jim Bowie or something.
(P.S. The reason you want a rock with good drainage is in case he pees.)