Over the last 30 or more years I've spent many, many days on various reservations mainly the Navajo and Hopi. Lots of good advise here especially observing rules and traffic laws.
I would add a few more suggestions. First and foremost is RESPECT! Don't ask questions especially about their religion or culture. You will be told what you need to know not what you want to know. Slow down and don't be in such a hurry. You might find yourself invited to a ceremonial dance or family gathering. Don't talk too much. Just listen. Be especially respectful of the elders.
A word of warning that should be adhered to. Do not drive after dark on the reservation unless absolutely necessary. There are too many horses, cows, dogs, pedestrians and impaired drivers.