Apply makeup. You can use makeup to create the illusion of a deathly pallor. A white/grey, purple or green tint works well for most people. Go to the drugstore and look for under-eye concealer or foundation base in these colors. Also purchase some dark eye shadow, eyeliner and baby powder.
Apply the base over your entire face and down your neck to get that unhealthy pallor.
Get directly under a light source and start using eye shadow to accent sunken areas of your face, such as your eye sockets and around the mid-way of your cheeks. Find shadows and darken those a lot.
Black out your eyes completely, but keep it under control. Make it look like your eye sockets have shrunken in about an inch. Get darker towards the middle and inside corners of the eyes, making sure to accent natural shadows but a bit more darker. (you can even try a darker gray shade; this sometimes works better for a realistic effect than black).
Use baby powder on your face to make your skin look dull and dead. Put a lot on so it looks like you're pale and dead and use some colors like pale light green or grayish-green eye shadow and apply it in some parts of your face and around the areas you had darkened. Lighten the color of your eyebrows.If you want to be a zombie you have to look as realistic as possible.
Apply solid red lipstick on parts where later you will apply your 'fake blood' on your lips and apply some dabs of purple or grayish or maroon lipstick to make it look like as if the blood is a bit dried and look more realistic.
If you want or can afford you can purchase contact lenses with the scary eyeballs. Well, most people think it is unnecessary to have them and any ways you can look scary enough even without these lenses but it's up to you to decide. There are many people who didn't use these on Halloween so there's no need to worry if you are not buying.