Measure the ottoman's dimensions and record all of the measurements: length and width of the top of the ottoman, and the height of the side of the ottoman (measure the side of the ottoman from the top to the bottom edge of the ottoman, not to the floor).
Remove the old fabric. Use pliers to remove any staples or nails, then use a utility knife if needed, to cut away any old fabric and trim. Try to leave the batting or cushioning in place where possible. Discard the old fabric, trim, and staples.
Stir the wood putty and spread a thin layer of it on the damaged wood or particle board on the ottoman's corners. Follow the manufacturer's instructions for use regarding thickness of layers and drying time. Repeat as needed to build up layers and restore the surface to its original shape.
Sand lightly if needed, to smooth out any dramatic ridges in the wood putty. There shouldn't be a noticeable difference between where the putty is and the wood or particle board above it.
Cover the ottoman with batting if needed or desired. Drape the batting over the ottoman, similar to wrapping a gift. You may use more than one layer if desired. Leave enough batting so that you can wrap it around the bottom edges and staple it to the bottom of the ottoman. Mark and cut away excess batting.
Begin stapling the batting to the bottom of the ottoman by starting in the middle of one side, and moving out to the edges. Fold the batting at the corners so that equal amounts of batting are on either side of the corner. Use the same technique on all four corners for consistency. Place staples about two inches apart for best results.
Staple the piece of old sheet or muslin over the quilt batting. This will keep the batting from shedding. This is not sturdy enough to serve as the upholstery for the ottoman, however. You'll need to use a slipcover, or, preferably, make a cover that you can staple into place like you did with the batting and muslin.
Install the slipcover or attach a new, custom-made ottoman cover, again, following the instructions for installing the muslin or sheet.