The author review fundamental aspects of the non-equilibrium Green function method in the simulation of nanometer electronic devices. The method is implemented into the recently developed computer package OPEDEVS to investigate transport properties of electrons in nano-scale devices and low-dimensional materials. Concretely, the authors present the definition of the four realtime Green functions, the retarded, advanced, lesser and greater functions. Basic relations among these functions and their equations of motion are also presented in detail as the basis for the performance of analytical and numerical calculations. In particular, the authors review in detail two . recursive algorithms, which are implemented in OPEDEVS to solve the Green functions defined in finite-size opened systems and in the surface layer of semi-infinite homogeneous ones. Operation of the package is then illustrated through the simulation of the transport characteristics of a typical semiconductor device structure, the resonant tunneling diodes.