Measure the wall or baseboard where you are installing the quarter round moulding using a measuring tape. Have a partner hold one side of the measuring tape and measure the distance to the other end of the wall. Use this measurement to mark the moulding to size with a pencil.
Place the quarter round moulding on the miter saw. Set the saw to a 45-degree angle. Cut the moulding to size with inside and outside corners at opposite 45-degree angles.
Set the quarter round moulding in place against the baseboard. Hold it firm while you nail it in place with a pneumatic brad nailer. Secure the quarter round moulding every 6 inches.
Fill the nail holes and cracks between moulding pieces with wood putty. Scoop a small amount of putty on your finger or a small putty knife. Squish the putty into the hole or crack. Smooth the top portion of the putty. Wait for the putty to dry and then lightly sand it with fine grit sandpaper.
Paint the quarter round moulding. Pour a small amount of paint into a paint tray. Use a paintbrush to carefully paint the moulding. Let the molding dry overnight.