Downhills!

A few simple rules may apply when riding downhill. You will want to keep your weight back on the bike, and maybe even off the back end of the saddle. Keep a firm grip on the handlebars, and your elbows low. Get a solid stance on your pedals, and a good grip on them with your shoes. Keep your pedals and crank arms even and parallel to the ground. Get off the saddle and crouch down for low center of gravity... you may want to lower your seat as well.
Scan the terrain well ahead, and be prepared for difficult areas in advance. Don't ride faster than you can handle, and slow down periodically by using the brakes a bit - control your speed.
Some challenging areas are best handled with some speed, however, and be careful of applying the front brake too much and either locking it up or skidding the front wheel if you get into a bind. Use your rear brake mainly, but do not allow the rear wheel to skid - incorporate the front brake as needed but do NOT allow the front wheel to skid!! If you must go down, go off the back or side of the bike, and not the front!! Protective gear (gloves, full helmet, knee pads, elbow pads, shin guards, etc..) are a good idea for the serious downhill rider, as well as a bike specifically set-up for downhilling.

The key to technical down-hilling is to relax your upper body.

The steeper and rockier the down-hill, the more tightly the rider grips the bar. A rider will slow down as they approach an obstacle, say a rock, applying both brakes as they go. However the rock will try to stop your wheel. If you have your brakes on, the brakes will try to stop your wheel, (I know this is obvious but hang with me for a while ok?)
A relaxed rider won't slow down quite as much, the combination of a little extra momentum, no front braking at the crucial moment and relaxed arms, allow the wheel to bump up over the rock and onward with little effort.So if you're going slowly, it's essential to let go of your brakes as you approach an obstacle.
This may mean going just a little faster, but the result is much less painful. I'm not talking high speed here, but let's face it, anything slower than a brisk walk is difficult on a smooth flat trail.

On a steep bumpy trail going really slow makes things very difficult indeed.
An exception to this is a very tight switchback turn. If a trials style hop is out of the question (it is for me!) you'll need to slow right down to allow the smallest turning circle. If it's very steep you'll also need to hang way off the back. This kind of stuff takes practice, track standing is a good way to improve your balance and it's one of the few 'street tricks' I practice. (It's not that I don't like them, I'm just rubbish at them.)