A stochastic lattice gas model is presented pertaining to classical charge transport in doped solid materials. Specifically, we investigate the diffusive dynamics of particles of charge q in an energy-landscape determined by immobile centers of charge - q which are distributed randomly in space. Results from extensive Monte Carlo simulations for tracer diffusion, conductivity and nuclear-spin relaxation are discussed and compared in detail with experiments on ion conduction in alkali-doped network glasses. Emphasis is put on the dependence of transport properties on carrier concentration and on non-exponential, slow relaxational effects which manifest themselves in different experimental spectra.