You might look at http://arxiv.org/pdf/math/0203100v1.pdf.  Moerdijk defines morphisms of orbifolds on page 8. The key is to link the map on the underlying spaces, with a morphism of the corresponding orfold groupoids. (i leave you to check a few pages earlier for the definition of them.)

Notice that they orbifolds are also stacks, and there is an extensive literature on them! :-)