1.a-The individual dies and rises again as a zombie through coincidental means such as proximity to a biological lab or meaningful date (Halloween, midnight, etc).
b-The individual dies and is resurrected as a zombie by a shaman, scientist or other meaningful (though usually malicious) individual.
c-The individual rises for purposes of plot and/or action in a larger story.
2. The individual dies of natural causes, but was posthumously infected and rises as a zombie.
3.a-The individual dies of the infection itself and rises as a zombie.
b-In some cases, the infection never kills the individual (see 28 days later).
A fourth and irregular clause is if the individual is born as a zombie, usually due to an infection of the mother (see Dawn of the Dead).
In order to distinguish zombies from other varieties of active dead they must have corporeal bodies and must be human. In some incidences animals have been infected (see Dawn of the Dead), though these can't be considered true zombies. There is much debate over whether or not a zombie has to have completely died for the zombiosis to have taken effect, though in such films as 28 Days Later the individuals were described as 'filled with rage'. In modern horror movies, mentioning the 'Z' word is considered by some a faux pas.
See also: zombie, undead, living dead, zombiology, zombification, zombified,