Examine the chair back, looking for the hardware that holds the back in place. Remove any screws with a screwdriver. Find the staples that hold the fabric on and pry loose the staples with a pair of pliers. Slide the edge of the pliers under the staple and lift up until the staple comes off.
Discard the fabric from the seat back and look at the foam. The foam adds padding to the chair, but it can also develop an odd or musty smell from food and other stains. Throw away the foam if it has a smell or shows any signs of mold.
Set the old foam on top of a new foam piece. Most craft stores sell foam specifically designed for upholstery uses. Trace the utility knife around the edge of the old piece, leaving the outline on the new foam. Move the old foam and cut along the outline you made, creating a new piece the same shape as the old foam.
Cover the foam with a piece of upholstery fabric. Trace the edges of the fabric with a black marker, creating an outline on the fabric. Cut off the excess fabric with a pair of scissors, leaving behind a piece of fabric to cover the foam.
Apply a thin layer of fabric glue to the front of the chair back. Press the fabric onto the foam, smoothing out any air bubbles with your hands. Turn the chair over and apply more glue to the back, attaching the fabric to the back of the foam.
Place the back on the kitchen chair. Hold the back with one hand as you screw the original screws back to the chair. The fabric glue takes the place of the staples, while the screws keep the seat from coming loose.