I've started riding 4 years ago, but at the begging I was struggling to make any signifficant progress. While there are many online resources, it can be quite difficult to apply all of those advice to the trail. However, these are the verified essentials that helped me to improve more in couple months, than I have previously managed to improve in years...
1. Attack position
This is the basic position in which you should be in to "attack" the trail. You have to be able to move freely around your cockpit and respond to any situation that can emerge. To get into good attack position you need to put your hips back and level your torso with the ground. This will put your head over the bars and force you to stick your elbows out (which is a good thing). By having your elbows out and arms relaxed, you gain another 10" of travel for free! Having your head low over the bars will also make you to keep your chin up to look ahead.
Shifting your butt back will force you to bend at your hips instead of your lower back. This way, with your knees slightly bent and heels down, you will drive all your weight into your pedals and through bottom bracket evenly to both your wheels. Finally, if you think you are low enough, get even lower!
2. Light hands, heavy feet
If you have your attack position right you should be nice and balanced between your wheels all the time. Imagine your pedals acting as a flying carpet which you stand on during the ride regardles of the trail slope. With your feet "heavy" you can keep your hands light, so even if you let go off the handlebars, you shouldn't be thrown out of balance.
3. Look where you want to go, go where you look
This one might sound easy, but it takes some practice to do unconsciously. You have to look and scan the trail as far ahead of you as possible so you have enough time to react to whatever the trail throws at you. The faster you go, the further you have to look. Again, if you have your attack position right, you will have your head up leading with your chin. You can practice looking far ahead every day when driving or walking around town.
4. Let go of the brakes
Face it, if you are not a pro racer, you probably drag your brakes a lot. I know I do it. Braking forces affect your bike handling a lot, so by braking excessively you do yourself a big disservice. Try to brake only when there is a real reason to loose some speed. Adjusting your speed for a corner is a good reason, being afraid of speed is not:) You have to work hard to get that bike moving so why would you want to waste all that energy? Look for good spots to brake and try to weigh the bike (push it into the ground) to get as much traction as you can while braking.
5. Pump it up
There is free speed everywhere on the trail, you just have to know how to use it. Make yourself light as a feather on the front side of the roller and become heavy on the backslope. You will be surprised how much speed you can pick up. Best way how to practice pumping is to ride on a pumptrack.
It's easy to relax when you are riding within your comfort zone, but as soon as things get hairy you tend to stiffen up. There is one small trick to get you relaxed - keep smiling. Try it now, your whole body will become much more relaxed as soon as you start smiling.
7. Ride with people both better and worse than you
It's obvious that better riders will inspire and motivate you to go faster and harder. But riding with and teaching other riders less experienced than you can help you even more. By teaching and explaining stuff to others you will realize your own mistakes and all those small pieces will come together.
One of the best MTB resources is a book written by Brian Lopes and Lee McCormack - Mastering Mountain Bike Skills. It's a must read book for every serios mountain biker. You can also find on Amazon.