A microscopic theory of the transport in a scanning tunneling microscope (STM) setup is introduced for pi-conjugated molecules on insulating films, based on the density matrix formalism. A key role is played in the theory by the energy dependent tunneling rates which account for the coupling of the molecule to the tip and to the substrate. In particular, we analyze how the geometrical differences between the localized tip and extended substrate are encoded in the tunneling rate and influence the transport characteristics. Finally, using benzene as an example of a planar, rotationally symmetric molecule, we calculate the STM current-voltage characteristics and current maps and analyze them in terms of few relevant angular momentum channels.