A new method is developed for study of photon- or electron-stimulated desorption from noninsulator surfaces. Concise and physically transparent, closed form expressions for the observables in a desorption experiment are given in terms of matrix elements of the interaction in stationary bases. The method is nonperturbative and spans the limits of weak to strong substrate-adsorbate interactions. We propose the possibility of relaxing several approximations frequently adopted in theoretical studies of desorption induced by electronic transitions. In particular, continuous decay of the transient electronic excitation produced by hot substrate carriers and the possibility of multiple electronic transitions follow naturally from the formulation and need not be introduced ad hoc. The description of time-delayed desorption, resulting from occurrence of predesorption resonances, entails neither conceptual nor computational difficulty and vibrational relaxation is consistently accounted for. The method is tested by application to an empirical model of the NH3/Cu photodesorption dynamics.