To kill zombies, you need to destroy their brains. The most surefire route is simply lopping off the cranium with a chainsaw, machete, or samurai sword. Mind the follow-through, however-- anything less than 100 percent severance just isn't good enough.
Any blunt object--from a baseball bat to a brick--wielded with suitable force at the cranium will destroy the brain. But be quick on your feet and keep your eye on the target, slugger--when you're this close to a zombie, miss even once and you might as well just hand your brains to the zombie on a silver platter.
Don't have the convenience of a sniper rifle to take out zombies from afar? The next best thing is a Molotov cocktail--just make sure the zombies are far enough away so they'll be reduced to ashes before they can shamble after you.
A solid technique, but one that requires heavy weaponry. In the chaos that will doubtlessly strike an urban center after a zombie infestation, make your way to a military storehouse or a morally dubious pawn shop and acquire a rocket launcher. Then shoot, load, and repeat.