This is the second of a series of papers which is devoted to a comprehensive theory of maps between orbifolds. In this paper, we develop a basic machinery for studying homotopy classes of such maps. It contains two parts: (1) the construction of a set of algebraic invariants — the homotopy groups, and (2) an analog of CW-complex theory. As a corollary of this machinery, the classical Whitehead theorem (which asserts that a weak homotopy equivalence is a homotopy equivalence) is extended to the orbifold category.