Meet the parents. Wherever possible, connect directly with parents as they drop off their kids, and try to add missing contact numbers to your list. Ask parents how kids will be getting home and jot that down as well.
Let your kids DJ. Okay, so you may have to listen to Lady Gaga and Kanye West over and over. Even if some lyrics seem offensive, there are more important things to worry about. Consider compromising here.
Feed the beasts. Keep it simple: pizza (wait to order until kids arrive so you have an accurate head count), chips, pretzels, soda (buy plenty—teens consume a lot), and maybe some cookies or other sweet treats. Avoid food that requires plates or utensils. Don't make our mistake of setting out wrapped candies or you'll end up with a floor full of sticky trash! If it's a birthday party, consider cupcakes instead of a cake for easy consumption. Remember to distribute large garbage cans throughout the space.
Make the rounds. Under the guise of restocking snack bowls, chaperones can take turns peering into any dark corners and checking on kids huddled outside. Some canoodling is to be expected (and essential to a successful party, from your teen's perspective), but maintain a PG-13 rating. If you see something suspicious—and this goes for signs of intoxication as well—discreetly talk to the kids in question. If need be, ask them to leave (this is where your parent contact list will come in handy). Just be sure to keep your teen informed to avert an embarrassing argument in front of guests.