Quarter-round molding is a thin strip of wood shaped with two flat sides and a rounded crest. This finish molding is commonly connected to baseboard trim along the floor to protect the wood and hide imperfections at the base. Usually nailed to the baseboard, it is possible to glue the quarter round to the wood to avoid nailing, filling the holes and painting over the repaired surface to hide the evidence of mounting.
Cut the quarter-round molding with a miter saw to fit the necessary length of the baseboard and for the appropriate angle joint needed. Test fit the molding to the baseboard, and draw a light pencil line on the baseboard to remember the height of the quarter round.
Scuff the side of the quarter round set to go against the baseboard with medium-grit sandpaper for about five strokes. Use the sandpaper on the baseboard below the drawn line an equal number of strokes. These uneven and scarred surfaces help the two pieces of wood bond better.
Apply two thin beads of liquid floor adhesive to the sanded side of the quarter-round molding. Align the molding against the baseboard and press it against the wood. Hold the quarter round in place for about one minute to allow the materials to form a bond.
Wipe away any adhesive that seeps from the quarter round and baseboard seam with a damp sponge.
Continue measuring, cutting, sanding and gluing the quarter round to the remainder of the room's baseboards. Allow the adhesive to dry overnight.