Mostly by car and pickup truck. It a is very rural area so pickups are preferred. There are very few buses, besides school buses, on the 16,000 square mile Navajo Nation.
There is no train. There are no public airports. There are some small landing strips for medical evacuation.
The nearest airports are of the reservation in Flagstaff, Cortez, and Farmington. And Most things are too far to walk. For example, from Kayenta on the western Navajo Nation to Flagstaff is about 2 hours by car.
To do any major shopping that is where one would need to go. (or a similar distance to Cortez or Farmington, or much farther to Gallup). Perhaps you mean how did people used to travel?
In the past (and up until the 1970s people sometimes still did) people used wagons and horse back. Before the 1540s- 1600s they did not have horses and they walked.
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