Decide how you died. This will be the starting point for playing a zombie. Did you die in a car crash with glass and bits of metal sticking out of your face, or did a heart surgery go wrong? Both of these ideas may be a bit more complicated than a heart attach or brain tumor, but make the most of the role.
Fashion a killer costume. Your costume should reflect how you died. If you are recently dead, some red paint or rips and dirt will do the trick. If you are long dead, you can have tattered, filthy clothes, maggots, worms and possibly missing limbs.
Apply the makeup. After deciding if you need to have a massive head wound, or your eye laying on your cheek, you will need to actually fashion the wounds and latex first. Apply the makeup on top of these. A great website to visit for all things zombie is Zombiemaker (see Resources below).
Grab a prop, or a buddy. Nothing is scarier than a zombie with an oral fixation. Play around with prosthetic appendages that you can gnaw on while playing a zombie. If you don't have a fake arm lying around, chew on your neighbor. (Make sure to get lots of fake blood to add some "realism".)
Work on the moan and shuffle. The undead are always moaning about brains. Try out some moans before you are asked to play a zombie. Find a convincing shuffle walk, as well. (Think of a drunk shuffle-walking to the bathroom crossed with an old man with a cane.)