Make sure you have the right materials and tools handy, and it'll go pretty fast. You'll need quilt batting, fabric (I used a fat quarter), staple gun, pliers, and scissors. Glue optional.
Cut out thee pieces of batting - one piece the same size as the seat, one piece a few inches smaller, then a third a few inches smaller than the first. Stack them on top of the seat with the largest piece on top.
Now place your fabric on the very top, making sure that there are at least three inches of overhang on each side.
The tricky part - flip the whole thing over without disturbing the layers. A bit of glue or spray adhesive could help, but for such a small project it wasn't worth the stickiness.
Starting at the center of each side, staple down the fabric, pulling gently but firmly to keep the fabric taut. Continue stapling around the edges, using the pliers to remove any whoopsie staples.
Secure the corners last, pulling the fabric in from both sides and stapling at least twice. Trim the fabric at the corners, and edges if needed.
Then flip it over - we're done! (If you really wanted to you could put another rectangle of fabric down to cover the raw edges, but who looks down there anyhow?)