Many interesting physical phenomena have been observed in electron-stimulated desorption studies of the cyanide molecule on alkali halide and alkali metal surfaces. We have performed a theoretical investigation of the nature of the cyanide-surface bond and of the desorption process using an ab initio density functional theoretic method of calculating electronic structure in the local density and Born-Oppenheimer approximations. We compare our results with experiment, and offer an explanation for an anomalous non-Boltzmann, temperature-independent rotational distribution experimentally observed in cyanide desorbed from these surfaces. As a verification of the method, we have performed extensive calculations on different bare alkali halide and alkali metal clusters and compared them with experimental results.