Honestly, it all depends on the game you play, or the book you read. There are many ways to ruin a zombies day, like:
-->Lop off it's legs and arms, leaving it as just a body and head (fun to watch for a while, until it tries to bite you) -->Fry it (fire) -->Make it immobile (freezing or cement)
But the chief way to destroy the zombie is to, as many people have said already, destroy the brain. The way a zombie get's infected can be from many different possibilities, like
-->A parasite, which lays eggs in the brain to reproduce. This type of infection can happen to any animal or thing with an organic-matter-composed brain.
--> A virus, which reproduces in the cells of the body, mainly the brain. This chiefly affects humans only, but has been known to affect dogs, due to their close proximity with humans.
However, all types affect the brain in some way, causing motor functions to fail within the body, the consiousness (both unconsious and consious, though mainly only affecting the consious), and the bodies other systems. In some cases, the human spirit can live within the unconsious mind in those who have strong immunities to the virus, or have been affected by a parasite. However, in most cases (exept for Sonny) the person cannot control their functions, cravings, or reactions.
There is, however, a more broad term for the word "Zombie." A zombie is considered, in some ways, "A Human puppet, brought back from the dead, to serve under a master, or under it's own influences. The crave for flesh is usually dominant, but the host can, in some cases, control those cravings for a time.
Many things can affect how a zombie acts during its time of reanimation. It's older self, the human still inside it, some thing to revoke memories in a brain that has not decayed yet, or strong wills, can make it into a "good" zombie. "Bad" zombies can be influenced through their masters, the virus or parasite's need for nurishment, or just it's older, if not criminal, self.
This is an almost full description of your general zombie. For more, look up "Zombie books" or "Zombie information" to see a more detailed description on zombies.
