  Taking an elementary and straightforward approach, we develop the concept of
a regular value for a smooth map f: O -> P between smooth orbifolds O and P. We
show that Sard's theorem holds and that the inverse image of a regular value is
a smooth full suborbifold of O. We also study some constraints that the
existence of a smooth orbifold map imposes on local isotropy groups. As an
application, we prove a Borsuk no retraction theorem for compact orbifolds with
boundary and some obstructions to the existence of real-valued orbifold maps
from local model orbifold charts.
