Riding a 4-wheeler is fun, no doubt about that. However, with the fun comes some responsibility. Both in personal safety and also environmental consciousness of all riders.
One way to practice "no trace" 4-wheeler riding is to stay on marked trails and never go trailblazing as most 4-wheeler trails are carefully maintained to allow riding on one area of a 4-wheeler trail and then periodically those trails are retired and the land is allowed to reclaim itself and different 4-wheeler trails are opened up. This careful planning and rotation of 4-wheeler trails insures that there are good rides for you now and future generations of riders.
Also, Treadlightly.org has published some fantastic standards for 4-wheeler riders that protect the land and wilderness and most are just mainly good old common sense. Learning proper handling techniques is a great way to help protect the land you ride your 4-wheeler on, a really big issue is many inexperienced 4-wheeler riders try to navigate hills and other inclines by going slightly sideways on their 4-wheelers, this not only wrecks the land beneath your wheels, it puts you in great danger of having your 4-wheeler, which weighs in the neighborhood of 200+ pounds, of turning over upon you.
Another careful consideration when riding your 4-wheeler is the navigation of creeks and streams, most 4-wheeler trails have carefully constructed crossing areas so there is minimal damage to the water areas.
Just use those basics and try to "leave no trace" on your next 4-wheeler ride.