Making a cardboard chair is a challenging but unique project. In an age of green movements of all shapes and sizes, the mantra of recycle, reduce, reuse, seems to be extending to all sectors of life—even do-it-yourself furniture. Cardboard is an abundant resource that has many similar properties to wood, and can lend itself quite well to the task of low-tech furniture building.
If you are considering undertaking this task, take a quick peek at designboom.com for some designs and plans. The site hosts a bunch of plans for different types and styles of cardboard chairs, along with pictures, and the dimensions required to build each model.
At the bare minimum you are going to need several cardboard boxes. Given your design choice, consider getting a variety of thicknesses. You will also need a box cutter (the sharper the better, as it will assist you in making nice precise lines), a straight edge, string, tape, wood glue (or other strong bonding agent), and a pencil or pen for marking.
Your enemy when working with cardboard is empty space. In order for it to actualize its load bearing capabilities, you need to make use of angles, closely packed pieces, and the rigidity of the corrugated interior structure. Some designs make use of a repetitive shape cut out of several cardboard surfaces, then glue them together, i.e. cut out the side view of a car seat (profile of the back seat and legs) as one piece. Repeat this until the glued result would be wide enough to accommodate a person. Wood glue is the best bonding agent for this technique, and using string or tape to hold the pieces together while they set is a good idea.
Other designs include using heavier gauged cardboard and cutting notches into the cardboard so that intersects with other parts perpendicularly, and utilizes the strength of angles to displace the weight provided by a seated individual. One with carpentry skills and a basic understanding of geometry would be best suited for this technique.