As is stated above, different breeds of zombies are killed in different ways. But it does not explain the complete METHOD for "How To Kill A Zombie". I will attempt to rectify this.

First, the Defensive Method For Killing A Zombie:

1. Get a phonebook/address book/directory/advice from someone you know to be living. Use this to find a gun shop.
2. Get a shotgun, with lots of ammo.
3. Wait for a zombie to come near the gunshop, but hopefully not WITHIN the gun shop. Shoot it with the shotgun, preferably in the skull. If it isn't dead, shoot it again. And again, and again, and again, until it is completely dismembered. If the smaller parts, such as the remains of the hands, do not continue moving, you may stop firing and continue on to another zombie. If the smaller parts keep moving, on the other hand,you have to keep trying to kill it, because now it's after you and it's pissed (if this breed has the capacity to be pissed).
4. Use whatever's handy to burn it, electrocute it, or contain it in a safe area (which you can safely run from afterwards in case it gets out). I'd suggest burning it with a match and oil, gasoline, or whatever else you have that's flammable. Electrocution can be done with electrical wires from home appliances, shop appliances, or telephone poles. Containing it... well, that's difficult. I suppose you could try to nail it to something with a nailgun, or you could try to squeeze it into some sort of large pet shop cage.
5. Overall, the rule is BE RESOURCEFUL. You have to find your own ways to shoot it, burn it, electrocute it, or contain it, as "whatever's handy" is much better than describing anything specific. The gun shop, however, is still the best idea.

The Offensive Method for Killing a Zombie:

1. Follow steps 1 and 2 from the Defensive Method for Killing a Zombie.
2. Run out of the gun shop, find some zombies, and shoot them! Shoot'em good!
3. Die a horrible, horrible death at the hands of the zombie horde, because going out and hunting large mobs of zombies is dumb. Really dumb.

I suggest using the Defensive Method if you wish to survive your own personal Night of the Living Dead, but either is a perfectly acceptable choice. Except the second one.