Answer: A bullet or a sharp blow to the head ought to do it. Or set 'em on fire.
How do you kill 'em? One of the humorous bits in "Night of the Living Dead" goes thusly: a field reporter (played by Bill "Chilly Billy" Cardille, local Pennsylvania DJ) asks Sheriff McClelland (played by George Kosana), "Chief, if I were surrounded by eight or ten of these things, would I stand a chance with them?" McClelland replies, "Well, there's no problem. If you have a gun, shoot 'em in the head. That's a sure way to kill 'em. If you don't, get yourself a club or a torch. Beat 'em or burn 'em. They go up pretty easy." And don't forget this line, which always makes me grin: The field reporter asks, "Are they slow-moving, chief?" Sheriff McClelland replies, "Yeah, they're dead. They're all messed up." [From "Quotes from Sheriff McClelland," on the Internet Movie Database website.]