Tunnel transport processes are considered in a square lattice of metallic nanogranules embedded into insulating host to model tunnel conduction in real metal/insulator granular layers. Based on a simple model with three possible charging states (+/- or 0) of a granule and three kinetic processes (creation or recombination of a +/- pair, and charge transfer) between neighbor granules, the mean-field kinetic theory is developed. It describes the interplay between charging energy and temperature and between the applied electric field and the Coulomb fields by the noncompensated charge density. The resulting charge and current distributions are found to essentially differ in the free area (FA), between the metallic contacts, or in the contact areas (CA) beneath those contacts. Thus, the steady-state dc transport is compatible only with zero charge density and ohmic resistivity in FA, but charge accumulation and nonohmic behavior are necessary for conduction over CA. The approximate analytic solutions are obtained for characteristic regimes (low or high charge density) of such conduction. The comparison is done with the measurement data on tunnel transport in related experimental systems.