Make sure you bring and drink at least 2 gallons of water a day in hot weather -- more if you're exerting yourself. Bring all the food you intend to eat, too. There are no restaurants at BRC.
Bring shade and shelter. You'll need at least a pup tent and a sleeping bag. It can get very, very hot and very, very cold at BRC -- often the same day. Dress in layers and bring and use sunscreen, a wide-brimmed hat and sunglasses or goggles.
Bring earplugs. It's noisy 24 hours a day and you'll want to sleep sometime.
Pace yourself. Too much exertion too quickly in the thin, dry air of the Black Rock Desert is potentially hazardous to your health. So is too much fun too quickly.