The time-dependent (TD) wave packet approach which we have been pursuing recently is extended to the calculation of state-to-state S matrix elements for reactive scattering in three dimensions for the H + O-2 reaction. Three specific methods for extracting state-to-state S matrix elements and reaction probabilities from the time-dependent wave packet propagation are specifically discussed in this paper. These methods are based, respectively, on the time correlation function expression for S matrix elements, scattering amplitude expression for S matrix elements, and flux formula for reaction probabilities. The implementation of these methods to TD reactive scattering is discussed and application to the resonant H + O-2 reaction is carried out to obtain state-to-state reaction probabilities for thousands of scattering energies.