We present a simple method to compute the transmission coefficient of a quantum system embedded between two conducting electrodes. Starting from the solution of the time-dependent Schrodinger equation, we demonstrate the relationship between the temporal evolution of the state vector, vertical bar psi(t)>, initially localized on one electrode and the electronic transmission coefficient, T(E). We particularly emphasize the role of the oscillation frequency and the decay rate of vertical bar psi(t)> in the line shape of T(E). This method is applied to the well-known problems of the single impurity, two-site systems and the benzene ring, where it agrees with well-accepted time-independent methods and gives new physical insight to the resonance and interference patterns widely observed in molecular junctions.