Some films skirt around the issue. Some attempt to attach a morality tale to it. Others address it firmly with nice solid answers from scientists in white lab coats. Why are the dead coming back to life?
Here are some of the main causes of zombie outbreaks, that may help add ideas for costume additions.
Radiation
A favorite of the cheesy italian horror of the 70s, radiation causes a particularly brainless and hungry zombie, with green ooze. Plenty of ooze.
Voodoo
The original zombies, in the historical sense, would be the product of Haitian voodoo. Be it the mystical powers of the shaman, or a cocktail of dubious Haitian powder slipped in the drink of a meddling American.
Cosmic Rays
If you are stuck for the mysterious cause, just put it down to cosmic rays / aliens, or something extraterrestrial. It's not unlike the radiation, often causing excess use of green ooze, but carries less morality tales about the dangers of advanced science and man's hubris.
Virus
A particularly popular one for the less credulous audiences of modern horror, viruses seem to have created some extra genre cliches. Gone are Romero's shambling zombies, and in come the sprinting wailing zombies. But are they zombies or just a bit poorly?
This gives great potential for nasty looking skin. Pustules are good, anything evoking the black death.
Toxic ooze
Drinking it. Swimming in it. Just spilling it accidentally. There's some nasty oozes out there, and they'll make a zombie out of you before you can wail braaaains in an expression of your everlasting unquenchable thirst for human flesh.
Once again, plenty of potential for green slime, and if you're being a zombie at night, some glow in the dark on the clothes is a nice touch.
Drugs
Morality tales again. This is tied somewhat to the voodoo powders, but more of the columbian marching powder variety. Take drugs and you'll become (more of a) zombie. Best not to use props for this one in public if you don't want a night at her majesty's pleasure.
The evil inherent in man
Some canny filmmakers don't need the obvious symbolism of drugs and foreigners to attach their great doses of cautionary tales about the downfall of modern society. The zombies are the symbolism. Geddit? Perhaps as good a cause as any other, but not so good for adding anything to the costume. A good cause for a scientist theme though, you were trying to discover the cause but got that bit too close to Bub...