In order to successfully begin killing zombies. Establish the following facts:

Who is directing the zombies?

If the zombies are being directed by George Romero, a simple attack on the brain of the creature will destroy them. Some people confuse this for any attack on the head and will be in for a nasty surprise when their knock to the head does nothing.

Examples of this can be found in the films Night of the Living Dead, Dawn of the Dead and Day of the Dead. The same vulnerability is found in other directors films such as Cemetary Man.

If the zombies are being directed by Dan O'Brannon, multiple possibilities are available but the same method will never work twice. Buring to ashes, Nuclear Attacks and Electricity are all used but in the end none of these function anymore as his zombies change every time.

You can see these methods in action in Return of the Living Dead, Return of the Living Dead II and Return of the Living Dead III.

Finally, if you are facing Voodoo zombies as opposed to actual walking dead, you will have to be far more cautious in your approach. Voodoo zombies are typically not actually dead, but are humans under the control of a hogan or Voodoo Queen. You may wish to avoid killing them altogether and simply subdue them or find an anti-toxin for the mind control potion that is usually used in these approaches. However, if you are an Action Hero, you can safely ignore this approach and kill as many as you like since the law never actually applies to you.