"Deadheading" is the rather strange term used by gardeners to describe the process of removing fading or dead flowers off of a living flower plant, encouraging the growth of more beautiful flowers.  However strange it may sound, it works!  As your blooms reach the end of their beauty, gently pinch them off the plant at the base of the flower (you'll find many will drop off into your hand).  Removing the fading blooms not only stimulates the plant to produce more, but it also keeps the plant looking fresher and cleaner.  Deadhead away!