Here are a few more additions that will keep you upright and enhance your mountain biking experience:
While keeping your head up and choosing a line, look where you want to go-- not where you DON'T want to go. This sounds obvious, but if you keep looking at that large rock or stump in the trail, chances are you will ride in to it rather than avoiding it.
Bombing the run through mud can be fun, but don't do this on public trails. When you ride through mud, you leave ruts. With continued abuse of the trail, you may come back one day to find it closed.
Riding up steep grades is easy with practice and traction. Avoid standing up and pumping the pedals to clean the hill. This may cause your rear tire to break traction, causing damage to the trail, and you to go horizontal. Instead, try selecting an easier gear before you begin the hill. Work on spinning, or pushing AND pulling up on the pedals throughout your stroke if you are clipped in. If you start losing traction, try pulling the handlebars back toward you, which will increase pressure on the back tire and provide your bike with a better grip. With these tricks, you can steadily roll right up a steep hill full of mud and gravel while staying in your seat the whole time.
The best way to avoid a flat is to bring along a spare tube, tire pump, and tire levers. Some kind of mystical force will work to save you from flats as long as you carry a spare. Also, you may encounter people that are as not as prepared as yourself, and you can fix their flat and greatly increase your karma.
Whatever you do, keep the future of the trail in mind. Don't tear it up. Don't litter. Give hikers and those on horseback the right of way. Yield to bikers going uphill. Believe me, I have seen way to many excellent trails close (or be closed only to mountain bikers) because of failure play nice.