  In this paper we study effective, nef and semiample cones of minimal surfaces
of general type with $p_g=0.$ We provide examples of minimal surfaces of
general type with $p_g=0, 2 \leq K^2 \leq 9$ which are Mori dream spaces. On
these examples we also give explicit description of effective cones and all
irreducible reduced curves of negative self-intersection. We also present
non-minimal surfaces of general type with $p_g=0$ that are not Mori dream
surfaces.
