Research the wide variety of camping chair kits available online and in camping and sporting goods stores. The classic camp chairs are made from wood and canvas, but today most models use aluminum, lightweight steel or plastic spars and various other fabrics. Prices range from as little as $25 up to $100 plus.
Read the instructions thoroughly before starting to assemble the camp chair. This is an essential first step, as often the parts of the chair must be assembled in a specific sequence. Almost always the frame is assembled first, then the fabric is fitted to it. It is often a good idea to lay out the parts in advance in the order they are going to be used.
If you are a more serious do-it-yourselfer and want to actually build your own camp chair from scratch, Scouters.us offers plans for a wood-frame chair. See Resources.