This video from Primitive Technology boils down the somewhat complex process of building a bow and arrows into a simple and information filled tutorial.
The following information was presented by the author:
The bow and arrows are made arrow using only primitive tools and materials.The bow is 1.25 m (55 inches) long and shoots 60 cm (2 feet) long arrows. The stave was made from a tree that was cut with a stone axe and split in half with a stone chisel. The string was made from the inner bark of a fibrous tree. It was separated into thin strips and left to dry. Then it was twisted into cordage.
Arrows were made of the same wood as the bow. A notch was carved into the back to accept the bow string and they were fletched with bush turkey feathers picked up from the ground. A feather was split in half and cut into 3 lengths then resin and bark fiber attached the fletching on to the arrows. The tip of the arrow was fire hardened and sharpened to a point. The fletching was trimmed using a hot coal. Each arrow took about an hour to make. A quiver was made of bark to hold the arrows.