Position one of the two pieces of molding to be joined into place on the wall, ceiling or floor. Put the second piece of molding into place, butting it against the first.
Hold the two pieces of molding in place, and scribe a line onto the first piece of molding using the profile of the second piece as a guide for your pencil.
Remove the two pieces of molding. Take the piece of molding with the pencil marks outlining the profile to a work table.
Hold a coping saw by the handle and place the blade against the wood so that the teeth are oriented toward the pencil line. Begin sawing back and forth, following the pencil line with the blade. As the pencil line turns, adjust the angle of the coping saw blade to follow the line until the profile in the molding has been cut.
Re-position the two pieces of molding on the wall so that the coped piece fits snugly over the un-cut piece of molding.