Important Note:
Zombies are quite hard to kill. Given that they have incredible physical power, you do NOT, I repeat NOT, want to be trading blows with them. Sometimes they want your delicious brains, which you probably want to maintain. Therefore, use the two most common zombie-killing methods:

Fire
Fire, for some reason, does massive damage to the undead. If you have a lighter, use it. If this does not work, and the zombie is slowly advancing towards you, look frantically for accelerants. If you are not in a toolshed and cannot find a conveniently placed container of kerosene, you are near screwed. Only one weapon left . . .

Long Bladed Weapons
Okay, so no go on the fire. You are probably now hearing the creepy music that usually foreshadows the addition of one more to the legions of the undead. Have no fear! Is there a rusty axe, chainsaw, or hopefully katana in the vicinity? If so, you can breathe a sigh of inappropriately timed relief. You want to dismember the zombie (head first, to disorient it) if using a axe, adze, or anything slow. When using a chainsaw or extremely sharp katana, get ready, 'cause it's time for fun. Slice the zombie in two, from between the arm and neck down to the waist. With any luck, your zombie troubles shall be over. Now kill all 500 other zombies, and you will be safe.