It’s widely accepted that zombies are driven by their brains, so the central nervous system must be functioning. And for movement to be possible at all, the peripheral system is also needed. But in zombies it appears that the autonomic system may be down, so the can devote more brain power to the needs of the central and peripheral subdivisions. This would reduce the amount of energy the zombie brain and body needs to function, potentially allowing it to survive longer with less.
So theoretically you should be able to destroy the central nervous system to render a zombie paralyzed. However, because so little of a Zombie’s brain is crucial to their survival, zombies can survive an enormous loss of brain tissue. Former FVZA zombie specialist, Dr. Waxman Himmelburger, tells of encountering a zombie who had lost over 3/4 of his head from a shotgun blast, with no apparent effect. Also, zombies have exhibited the ability to withstand significant trauma to their central nervous system.
So in my opinion the best way to kill a zombie would be to completely sever their spinal cord and/or completely destroy their brain.
Shooting them in the correct places could do this, and shooting them could definitely slow them down if you are able to remove a limb or two.
But here would be the best ways:
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.