since how long have these tribes worked in this weaving industry?
early 18th century.
Navajo weaving
Written records establish the Navajo as fine weavers for at least the last 300 years, beginning with Spanish colonial descriptions of the early 18th century. 
what kind of tools did the navajo tribe use UNANSWERABLE in which regions are these tribes found? Four Corners area of the United States. what places come under that corner area? The Four Corners is a region of the United States consisting of the southwestern corner of Colorado, southeastern corner of Utah, northeastern corner of Arizona, and northwestern corner of New Mexico. what materials did those tribes use to weave their products? three-ply yarn and wool is there any special animal breed from where they source the second material? Rambouillet rams what were some of their finished products after weaving? handwoven blankets and rugs what dyes were used to color their products? Yes what equipment/machines did they use to weave their products? Traditional Navajo weaving used upright looms with no moving parts. Support poles were traditionally constructed of wood; steel pipe is more common today. what was special about the design of their finished products? Many of these patterns are historically handed down from one weaver to the next generation of weavers who live within the same area.
wiki:15389300
Navajo weaving [SEP] Early records
Written records establish the Navajo as fine weavers for at least the last 300 years, beginning with Spanish colonial descriptions of the early 18th century. By 1812, Pedro Piño called the Navajo the best weavers in the province. Few remnants of 18th-century Navajo weaving survive; the most important surviving examples of early Navajo weaving come from Massacre Cave at Canyon de Chelly, Arizona. In 1804, a group of Navajo were shot and killed there, where they were seeking refuge from Spanish soldiers. For a hundred years the cave remained untouched due to Navajo taboos until a local trader named Sam Day entered it and retrieved the textiles.