There are books and magazines dedicated to trail running.

Here’s a few very brief tips:

Be quick, light and nimble on your feet. The less time your feet are on the ground, the better. The lighter you land, the less chance of stumbling. This is also great for road running (i.e., trail running will make you a better/more efficient on roads).

Uphill, you need more drive from your hip, and more backwards swing of your arms. The arms will help drive your hips forward. Look up the hill, not into it. Keep your body in allignment; don’t bend over at the waist. It takes more power to drive uphill.

Downhill, when it’s steep and/or technical (loose, rocky), use very short and quick steps, like running on hot coals. Stay on the balls of your feet. When it’s not steep or technical, it’s OK to let gravity carry your stride longer, but keep your foot plant under you. Continue to keep your hips forward. DON’T LEAN BACK! You don’t have much control on you heels. Much of downhill is confidence. Your body naturally does things to resist falling, like leaning back, but staying forward is more efficient. You won’t fall if you keep your legs moving (OK, it is riskier than a flat road). Slow yourself down early, and only go as fast as you are comfortable. It takes time to become comfortable downhill.

Mainly, you need to go run on trails. That’s very hard to do in these conditions (though many of us crazy people continue to do so). Any uneven or unstable surface will simulate trails. So, running on the snow covered Highline, the packed trail around Wash Park, or the snow/ice covered bike paths can be good training. Snowshoeing is also an excellent way to get out on trails.

References:

+ Ultimate Guide to Trail Running, Adam Chase and Nancy Hobbs

+ Chi Running, Danny Dreyer. How to use energy more efficiency. Includes sections on Trail Running.

+ Pose Method® of Running, Dr. Nicholas Romanov. Not specific to trail running, but great drills, and great illustration of general techniques that apply to trails as well as roads.

+Running with the Whole Body, Jack Heggie. Great form ideas and drills.

+Trail Runner Magazine. Available at running stores, book stores, and online.
When in doubt, run uphill!