Remove the existing chair cushion from the seat itself. In most cases it will be screwed into position, so turn the chair upside down and use a drill or screwdriver to unscrew the seat from the chair frame.
Use scissors to cut the fabric off the chair seat base. Pull the rest of the fabric off and inspect the padding on the chair. If it is in decent shape you could reuse it; if not, pull it off with your hands. If the fabric is stapled to the base of the seat, use a flat screwdriver or pry bar to remove them as well.
If you removed the old padding, cut a new piece of padding that is one to two inches thick and the same length and width as the chair base itself. Use glue to attach the new padding to the chair base. If you left the old padding in place, omit this step.
Cut a square of fabric that is three inches longer and wider than the chair base. Wrap the fabric over the top of the chair base and foam padding, pulling the sides around to the bottom of the chair base. Staple the edges of the fabric to the underside of the chair base, starting with one staple on each side and then moving around the entire base to secure all of the fabric edges.
Reattach the seat base to the chair frame using the same screws you removed in the first step.