Check out the TrailForks site for a listing of local trails in the Yellowknife area!
Staying on marked trails reduces the ecological damage to the environment. The NWT is home to some beautiful, and very delicate lichens which take a very long time to grow!
Be a good human, don't run anybody over out there.
Don't litter, pack out whatever snack wrappers or other garbage you might have.
Consider volunteering some time to build and maintain existing trails. This can be as simple as trimming the willows of a trail corridor on your next hike!