Here are a few essential skills needed for general mountain biking. You probably have a few of them down, so just work one that you may need practice on.
Looking ahead: This is the single most important skill in mountain biking. Most new people to the sport only look a few feet ahead which can be disastrous in this sport. There are so many obstacles on a mountain biking trail that can and will throw your balance off and can send you down before you know it. Like diving, your looking way down the road, you do not look near the hood of your car. The faster you go, the farther down the trail you should look, your peripheral vision will assimilate the object near you and with experience, you will naturally pick the best line.
Staying loose: Depending upon the bike that you have, you will need to use part of your body to absorb some of the trails obstacles, dips, bumps and transitions. Have a firm grip on the bars and loosen up your body when on the descent, flow with the trail and allow your bikes suspension to do most of the work and you'll provide rest. In mountain biking, you want to have agility as you weight is constantly shifting front to back and left to right. Be loose and fluid.
Use the front brake: Most people that are new to mountain biking use the back brake more than the front. While this will work, it is not the most efficient way to brake a bike or car for that matter. If you look at most cars and motorcycles, you will notice that they have a larger rotor on the front then on the rear. A larger rotor has more efficient stopping power over a smaller rotor.
When you start applying brake pressure to your bike (or any vehicle) the bulk of the weight shifts towards the front of the bike. That is where you need most of your braking power, where most of the weight is. One thing a lot of new bikers are worried about when applying a lot of pressure to the front brakes is going over the handlebars. The way to make sure that you do not do this is to shift your weight to the back of the bike if you are braking hard. You will also want to brake when you are on a straight line and before a turn, not on the turn.
In general, you can initiate braking by applying the rear brake then squeezing the front until you get the desired braking power. Counter the weight shift by slightly leaning your weight to the rear of the bike. Practice!
Shifting: You will want to anticipate that uphill climb by shifting into a gear before the ascent that will enable you to pedal through. When you are climbing and need to shift, there is a lot of chain tension between the front and back which places a lot of stress on the derailleur makes it difficult to shift. You will also have increased chain wear by forcing a shift while pedaling uphill. Ideally, you will want your chain to be in a straight line from the chain ring up front to the rear cassette. Your chain will last longer as you will not have as much wear due to cross chain friction.
Elbows out: Most people that are new to mountain biking are riding them just like the road bike that they had in high school. If you want to ride aggressively on your local trail, you need to be in the attack position. This is where you are off of the seat and your weight is dividied 50/50 between the front and rear tires. The position allows you to move your weight to the front or back in a split second when needed. In this position, your elbows are pointing outwards, not back and near your body. If you have ever done a bench press, could you press a lot of weight with your elbows in?
Bunny hop: You can practice this in your front yard or near the trail-head. It is a must have skill for mountain biking as you can jump small objects on the trail without running over them. A fallen tree branch or a small section of rocks can be bunny hopped to get around the obstacle.
Clipping in: In general, most riders have trail bikes or cross country bikes with clip in pedals. You will want to practice clipping in without looking down. If you un-clip for a technical section, you should be able to clip in right away and continue on. Some pedals come with two sets of clips, one that is easy to clip out (15*) and another that is a bit harder (30* heel angle). You will want to use the 15* if your new to clipless.
Breathing: For those uphill climbs, most riders will just breath a little harder than usual due to the exercise. One thing that you can do on those climbs is to exhale as much as you can (carbon dioxide) from your lungs so you can bring in more oxygen. The more oxygen you can take in will allow more to your blood-stream and to your working muscles which will enable you to be more efficient.