Apply a drop of wood glue to the end of a putty knife. Apply the glue by slipping the end of the knife under splinters to saturate the area. Wrap the area with masking tape to compress splinters back into place. Allow the glue to dry overnight.
Scrape off any dried glue, broken chips or debris with the putty knife. Scoop a dime-size amount of wood filler out of the can with the putty knife. Apply the filler into pits, gouges and scratches with enough force that the filler expands upward from the damage.
Apply more filler to the damaged area, troweling it over the damage to cover it completely. Apply more filler if needed to restore the damaged area slightly larger than its original size. Allow the filler to dry completely.
Shape the filler by sliding a medium-grit file along existing profile lines, creating similar profile lines in the filler. Fold a piece of 100-grit sandpaper into thirds, use the folded edge like a knife to define lines, cracks, corners and edges, restoring the damaged area to its original shape.
Roll a piece of 100-grit sandpaper around rounded parts. Rotate the sandpaper around the damaged area to smooth. Roll a piece of sandpaper around a 1/2-inch dowel. Use the dowel to sand curves in the filler if needed to match the profile. Sand the repaired area again using 120-grit sandpaper.
Apply a matching oil-based stain to the entire leg, runner, arm or piece of furniture including the repaired area using a folded piece of cotton cloth. If the furniture has a natural finish skip this step. Allow the stain to tint small scratches or lines in the existing clear finish on the furniture that might have occurred during sanding. Oil-based stain colors scratches to hide them. Wipe off any extra stain with a dry cloth. Allow the stain to dry for 72 hours.
Add matching paint if the furniture is painted, and not stained. Apply a single coat with a brush and allow it to dry. Lightly sand the area using steel wool. Apply another coat.
Apply a light coat of clear finish to the repaired area and allow it to dry. Sand the area lightly with 120-grit sandpaper. Apply another coat of clear finish.