How does Artificial Selection work?
Both natural selection and artificial selection require genetic variation in the underlying population to work.  The exact source of this genetic variation is not particularly important theoretically.  In reality this genetic variation originally comes from mutations of various sorts (not just point mutations, but also duplications, recombinations, etc.).  If you had no genetic variation then artificial selection would not be effective.

You might be interested in Stephen Jay Gould's essay "A Dog's Life in Galton's Polyhedron" (found in the collection "Eight Little Piggies"), where he explains that domestic dogs have very little variation in skull length (relative to body size), but large variation in skull width.  It seems that it is very difficult to artificially select for dogs whose skull and body don't have the correct ratio, even though you can wildly change the sizes of dogs, the width of their skulls, the length of their legs, etc.