Remove loose pieces of rotted siding or dirt from the hole before applying patching compound.
Fill in the holes in your hardboard siding with patching compound, using your sheetrock finishing knife. Scrape off any excess compound. The size of the sheetrock finishing knife depends on the size of the hole. Allow the compound to dry completely before sanding or adding another layer.
Sand the patching compound once it has dried and wipe off the dust with a damp cloth. For larger holes, add another layer of compound, and then let it dry. Sand the area again to smooth it out, and then wipe with a damp cloth.
Paint the patched area with two to three coats of paint that matches the color of your hardboard siding. Allow paint to dry completely between each coat.