Pre-ride or Walk the Race Course
Not only will it let you best know when to hammer and when to catch your breath, but it can also let you work out the best approach in advance for the technical or unexpected parts of the trail that could otherwise have caused a spill.
Replace What You Burn
Drink fruit juice in large quantities to replace the calories and water lost during the race. For races lasting less than an hour, plain water can suffice, but for longer rlaces it is essential to replace calories, or you will "bonk," or become extremely exhausted when your body's carbohydrate reserves are used up, as fats alone can't supply enough energy to keep a reasonable pace. Drink about 750 mL (one large water bottle) per hour, which replaces the water you lose and supplies about 270 calories per hour (less if watered down). Eating solid or gelled sports foods (or cookies and granola bars, for that matter) are also good sources of calories, but sucking OJ from a camelbak is the only hands-free way to replace both calories and water.
More information on Eating and Drinking on long bike rides is found in the nutrition section, which also caloric data on lots of foods and drinks, and much more.
Carry Spare Tools
Have a spare tube or patch kit and mini pump, allen keys and tire levers at a minimum. Punctures are more common on mountain races than on road races, even with the lightweight tires, so don't think it won't happen to you (or your buddy). You should also corry a chain tool, cables, swiss army knife and a spoke wrench. It's not a question of if you will need them, but when. Don't give yourself a two hour walk because you left your chain tool at home.
But, obviously, get your bike dialed before the race so you can reasonably hope to not need them.
Watch the Other Races
Aside from being entertaining, you can learn a lot about technique by watching the more experienced riders.
Sprint at the Start
It is very difficult to pass on singletrack, so the first people to make it it the singletrack have a huge advantage over the rest of the field. Sprint, and seize the opportunity to get ahead of your competitors. Moving your seat forward and lowering your handlebars will give you an advantage in the sprint.
Wear Gloves and Shorts
Bike gloves will absorb shock from the trail very nicely, prevent sore hands from the handlebars, and they are a godsend for soaking up the roadburn that otherwise would have grated your hands and elbows into a bloody mess. Bike shorts will wick moisture away and will also absorb shock and make the ride more comfortable for your seat.
Chances are that your next race won't be the world championships, but a local race where people go out because it's fun. Riders will make mistakes, as will you. Slower riders may get to the singletrack first and be difficult to pass, but that doesn't give anyone free license to be a jerk to them! If you would like to pass, simply wait until there's room and politely say "track right" or "I'm passing on your left." The point of sports is to have fun, so leave the attitude at home and go have fun!