Turn your stool upside down and remove the screws on the four corners of the underside of the stool top. Set the screws aside in a safe place and remove the base of the stool from the cushioned stool top.
Lay your fabric right side down on a flat surface. Place the stool top on top of the fabric. Draw around the perimeter of the stool top, approximately 3 inches away from the edges, with the pencil. For this project, the measurements don't need to be exact, but there does need to be sufficient excess fabric for you to wrap the fabric underneath the stool top.
Cut the fabric on the line. Center the stool top, right side down, on the fabric. Pull the fabric tightly up and over onto the underside of the stool top and staple the left side into place with one staple. Pull the right side tightly up and over to the underside and staple into place. Add at least two more staples to each side to secure the fabric. Repeat with the top and bottom sides.
Tuck the excess fabric at one corner neatly so that it lays flat. Pull the corner tightly and staple into place. Repeat with each corner. Turn the stool right side up before you staple each additional corner to ensure they look the same and adjust if necessary.
Trim any excess fabric from the underside of the stool so it looks neat and clean.
Place the stool right side up on top of the base and center it so it lays flat. Hold the top in place and flip the entire stool upside down so you can see the screw holes on the underside. Place a screw in one corner and screw in place. Screw the next screw in the corner diagonal from the screw you previously placed. Continue in the manner until all the screws are in place. Turn your stool right side up.