First you use a band saw to cut MDF plywood into the shape that fits the seat's template. Then you staple synthetic polyester strips (technically polyethylene terephthalate, commonly called by brand name Dacron) to make a sturdy yet giving center part of the seat.
Next you put a foam cushion over the seat frame. Big, thick foam that is made to be resilient even after lots of sitting.
Then choose the leather or fabric covering you want for your seat.
Cut the fabric and wrap the seat with the fabric.
Pull the fabric tight around the cushion and frame. Or if you're fancy, use a seat press that applies pressure and makes upholstering the seat easier.
Now you have a completed seat.
Put the seat on a chair. Voila!