The red lines are quillwork, made with porcupine quills. This technique was used for hundreds of years before beadwork became popular in the 1800s with glass beads from Venice.
These kinds of triangles are called step triangles.
The dark blue shapes are called buffalo tracks, space or part-between.
Tripe design.
“Two-color, elongated diamond shapes are usually called the Feather, Whirlwind or Breath of Life design.”
Four directions
Women of several tribes started making moccasins with beaded soles in the 1880s.
“Twisted design” (beads in diagonal checker rows)
Box designs. The squares often represented bags.
Boxes with inverted triangles were common in the Shoshone tribe, therefore known as Shoeshone design.
All images and information from Wyoming State Museum’s Beautiful Shoes (2012) which also explains different techniques, and the same museum’s moccasin page at Göögle Arts & Culture.