How can I minimize the effect my riding has on the trails?
First, it's great that you recognize that how you ride off road has consequences. Bravo. Having a conscience like this is the first step in riding responsibly. And, you're obviously far-sighted enough to realize how important responsible trail use is in cyclists gaining and keeping trail access.
The secret to trail preservation is practicing what's known as soft cycling. This is as much a mindset as a riding technique. It's being considerate of the trail and other users. It's constantly monitoring how you're riding. It's being in tune with your surroundings. If you can learn to ride like this, you'll minimize the effect your rides have on the trails -- and hikers and equestrians. Here are some rules followed by soft cyclists:
Follow the trails and stay off obvious illegal detours that lead down steep sections or across shortcuts because these increase erosion, which damages the trail.
If the trail is muddy or blocked, don't ride around the problem. You'll only widen the trail in the process (a big negative in the eyes of land managers, who hold the key to our trail access). Instead, dismount and walk. This slight inconvenience will preserve the trail for all.
Practice restraint. We know it's fun to blitz trails at warp speed. But, it often leads to losing control, skidding, even crashing. And these actions erode trails. Plus, what if a hiker or equestrian is around the bend? Disaster! Not to mention the ripple effect of the negativity this creates with the startled (perhaps injured) person who's sure to tell every friend about the inconsiderate cretin who nearly flattened him.
In the wet seasons, when the trails are most vulnerable, consider riding the road. You'll enjoy the change in routine and the trails will have a chance to dry out. Plus, the extra wear and tear that mud, grit and water exact on your bike can be expensive.
When riding, if you spot some debris, especially bike refuse (reflector, tube, energy-bar wrapper, etc.), pick it up and take it home. Better that, than leaving it there to trash the trail, annoy other users and prejudice them against off-road riders and riding.
Likewise, if you come upon something blocking the trail, a downed limb or small slide, that can be easily moved, by all means, stop and do your share to keep the trail shipshape.
Finally, consider stopping occasionally and enjoying a scenic overlook or shade tree to remind yourself why it's so important to respect trails and ride softly.