A relatively simple and straightforward procedure for characterizing molecular wires is to measure the conductance spectrum by forming a self-assembled ordered monolayer (SAM) on a metallic surface and using a high scanning-tunneling microscope resolution (STM) tip as the other contact. We find that the conductance spectrum (dI/dV vs. V) can be understood fairly well in terms of a relatively simple model, provided the spatial profile of the electrostatic potential under bias is property accounted for. The effect of the potential profile is particularly striking and can convert a symmetric conductor into a rectifier and vice versa. The purpose of this paper is to (1) describe the theoretical model in detail, (2) identify the important parameters that influence the spectra and show how these parameters can be deduced directly from the conductance spectrum, and (3) compare the theoretical prediction with experimentally measured conductance spectra for xylyl dithiol and phenyl dithiol.