See if any of these make sense (Google for "Parametric Surface" for others) :-
http://www.math.duke.edu/education/ccp/materials/mvcalc/parasurfs/para1.html
http://en.wikipedia.org/wiki/Parametric_surface
http://cs.jsu.edu/mcis/faculty/leathrum/Mathlets/parasurf.html

It was straight forward in this case as x and y are just scaled version of u and v, for other non-parametric surface definitions, things will be trickier.