Artificial propagation methods

The most common are by taking cuttings and rooting them (usually with the aid of a rooting hormone), and grafting (which is more involved, and more difficult to do.)

google "plant propagation techniques"

A couple of sites with good info that I've used are:

http://www.rainyside.com/archives/cuttings.html

http://gardening.about.com/od/gardenprimer/ss/Cuttings.htm

www.plantpropagation.com