In many places trapping or shooting fur bearers require a licence. Nuisance beaver may be the exception however. If this isn't an issue then as far as getting one easily, by all means, open a dam and sit there in the evening. But make your shot a clean kill or you won't get him. He'll dive and you most likely won't see where he comes up--usually in his house. Then the other beaver in the lodge will chew him and your potential hat, to a rats ass.