Turn the chair or stool over and use a screwdriver to remove the screws holding the seat in place. Set the screws aside. Use a staple remover or tack remover to take the old covering off.
Place the fabric on a table or the floor with the right side--the side you will see when the cushion is finished--down. Place the seat cushion upside down on the fabric.
Trace around the seat cushion with a fabric marker to make an outline. Measure the depth of the cushion and add 3 inches. Using the tracing as your starting point, draw the outline of the cushion cover by adding to the tracing the number of inches you calculated and drawing a new, larger outline.
Cut out the seat cushion cover with scissors or a rotary cutter. Place the seat cushion on the cushion cover using your first, smaller outline as a guide.
Start at the center front of the seat cushion to staple the cover to the wooden base of the cushion. Pull the fabric over the cushion so that it is taut but not tight. Use a staple gun to attach the fabric to the seat cushion at the center. Repeat with the back and the two sides of the seat cushion cover. You should now have four staples holding the seat cushion cover to the seat cushion.
Form a neat corner by pulling up the middle of the corner of the cover and folding the extra fabric at each side to bring it neatly to the back of the cushion. Staple in place. Repeat with the other three corners. Finish stapling the cover to the cushion by placing staples every 2 to 3 inches along the perimeter. Trim away excess fabric from the bottom of the seat cushion using scissors.
Reattach the seat cushion to the chair using the screws you removed in Step 1 and a screwdriver.