Spread the 2-by-3-foot fabric out on a flat surface with the pattern facing down. Place the foam over the fabric. Center the foam so the fabric sticks out by 6 inches on all four sides.
Place the board over the foam and align the edges. Lean on the board and pull the fabric upwards and to the top of the board along one long side. Staple down the fabric every 2 inches until you are 1 inch from the corner. Repeat this step on the other long side and the short sides.
Pull each corner of fabric upright and bring it to the back of the board. Smooth the fabric as needed to make the surface of the fabric flat. Staple two to three staples to hold each corner down.
Spread the other fabric on a flat surface with the pattern facing down. Fold in each side by a ½-inch and iron the fold. Sew along the fold to hold it in place and hem the material.
Apply a line of hot glue along each edge on the top of the board. Press the hemmed fabric to the back of the board with the pattern facing up to cover the edges of the first fabric.
Turn your wooden stool upside down and set the seat of the stool against the fabric covering the board. Center the seat as needed over the board.
Drill through seat and into the board with four woodscrews spaced evenly apart about 1 inch in from where the legs attach to the existing stool seat. Flip the stool over.