Measure the length of the threshold of the sliding glass door with a tape measure on the interior side of the door.
Lay the quarter round molding on the table of a miter saw. Measure and mark it to the length that you measured in step 1 using a tape measure and pencil.
Cut the quarter round to length using the miter saw. Sand the ends of the molding with a fine-grit sanding pad until they are smooth.
Lay the quarter round molding on the floor in front of the interior side of the sliding glass door threshold. Fit it tightly against the threshold and hammer finish nails through the molding into the floor every 6 to 8 inches to secure it in place.
Center a nail set over each nail head and tap it with a hammer to set the nails 1/16 inch below the surface of the threshold. Fill the nail holes with wood putty using a putty knife. Allow the putty to dry for 24 hours.
Sand the putty flush with the surface of the wood in the same direction as the wood grain.
Brush two coats of wood finish onto the quarter round molding using an angled sash paintbrush. Allow the finish to dry four hours between coats.