Green function and density functional theories are used to study electron transport characteristics through single molecules addressed by two metallic contacts. Each contact is modeled with one nanoscopic end connected to the molecule and one macroscopic end connected to an external potential difference. The method can be applied to any molecular system for which ab initio calculations can be performed. It allows us to determine the molecular orbitals participating in the electron-transfer process, the current-voltage characteristics of the junction, the density of states, and the transmission function, among other properties, providing a fundamental tool for the development of molecular electronics. The method is tested with Au-n-S-(p-C6H4)-S-Au (n = 1-5) connected to bulk Sold. Current-voltage characteristics are in excellent agreement with a break junction experiment and with other ab initio calculations, yielding new insights regarding electron transport through single molecules.