*cracks fingers*
Stay awhile and listen...
First off, sometimes with zombies, less is more. Your going to need some black and white make-up and one of those triangular sponges woman use to blend their make-up (that's the key, really. The blending...). Now, you can also use a little green and even some blue mixed with a ton of white to get that nice cold look.
Next up, of course, is the blood. Most stage blood now is ok if your kids are going to be eating it. But make sure you get the right kind! There's a type thats quite thick and sticky, and most importantly, doesn't coagulate. (dry up and flake off) I got a few costume shops around my place that carry it, it's not exactly dollar store brand cheap, but for the extra few bucks I think you get a more authentic zombie.
Wanna really get a cool look? pick up from a dollar store or zellers or wallmart some fake skin. A couple dollar store in my area have them every year and it's a buck for a little plastic tin of it. Even though it's a small amount you can actually do quite a bit with it. More on that later...
Make-up applications:
If your using the fake skin, put it on before any make up. You can use it pretty much any ways you like, but what I like to do is grab the wad of skin and pull it apart until it tears away (it's usually all stringy) then basically put it on your face just like that. It adds texture and decay, but the trick is, tearing up so it's a nice thin "sheets" that way it will stay stuck to your face. you can layer it as necessary, but it's the make up over it that really makes it work.
Darken up the eyes with some black make-up and use your little triangle to blend around the cheek bones and outside corners. Bring the black up basically to just under the ridge of your eye socket. Use a little bit of black in the cheeks to get that "sunken" look. Use very little though, and blend, blend, BLEND.
Use the white or the white/blue blend to highlight the forehead and cheekbones. If you used the fake skin from earlier, but a bit of black on the skin first and blend it around to get it inside the cracks and crevases. Then use a little green to highlight the tops of the scar.
Blood application is the real show stopper though, even if you fucked up all the make-up you can still salvage the costume with a good bloody mouth. The single item you need is this little sponge http://media.hauntedprops.com/v/vspfiles/photos/19304-0.jpg in that pic it's the black square. That little guy is gonna make all the difference. put some of the blood on the sponge and then DAB all the areas you want bloody. it should stick your face as little droplets, some of which will meld together. I advise putting blood all over the mouth area, down the neck, and just off to one side of the mouth/neck area (blood gush from initial bite)
I'll add more later...but I gotta work now.