Halloween, my favorite holiday because I can scare the holy piss out of the neighbor kids without getting arrested
As you know a zombie is a reanimated corpse, so you gotta look like you've been dead awhile.
You want grey pancake makeup and either green or blue pancake makeup. Green is the more traditional zombie color but I like blue better because that's the color a dead guy's skin will turn if the embalmer doesn't use makeup on him. You also want a natural makeup sponge. You can get all this crap at the costume/magic shop, and the clerk can usually give you tips on applying it. Lightly sponge (dab the sponge on your face, DON'T smear or wipe it!) on a grey base (don't cover the entire skin), then move to the color, then a little more grey, then a little more color. You'll end up with a creepy rotting flesh effect that will have natural-looking light and dark areas, just like a regular face. If you get too much on there or you "paint" it on you'll end up with a shiny face or a plastic looking face, and that's no good. Be sure to get your neck and ears too or it'll look really dumb. Do the neck at least 4 inches below where the collar of your shirt will hit.
Black lipstick and eyeliner, and some talcum powder in your hair (assuming you're dark haired - if you're blond/red and want to go all out do some temporary hair color - - it washes out after 5 or 6 showers) will complete the face. If you're ambitious you can move to your hands too - - but leave the palms alone or you'll drip all over everything.
If you're REALLY ambitious costume shops sell prosthetics that can make it look like the flesh is melting off your face. Apply the prosthesis first (wash your face unbelievably well, then glue it on with spirit gum), then the makeup.
Now a white longsleeved (unless you makeup the arms) Tshirt, collarless if you can find it, dyed a dirty grey and ripped to shreds (not too much ripping or your regular skin tone will show underneath and ruin the effect- - unless of course you're insane like me and do the makeup on your torso too
Otherwise wear a black tshirt underneath the white one to hide your skin), and some torn up and dirty jeans/slacks will complete the look.
Believe it or not this is a very simple zombie effect. If you went all out you'd have latex pieces all over your face to make it really look good - - but the trouble with latex pieces is that they get hot, and you sweat into them, and it's uncomfortable. That's fine if you're doing a haunted house because you're going all out but if it's a party or something, it makes it less fun. Plus a corner of the latex inevitably comes unglued and then all the sweat runs down your face and wrecks more stuff. . . yeah, you get the idea