The adsorption of weakly charged polyelectrolytes at planar and oppositely charged surfaces was modeled by using a mean-field lattice theory for flexible polyelectrolytes in solution. The nature of the adsorption was described in terms of volume fraction profiles, adsorbed amount; thickness of adsorbed layer, and conformational characteristics at different salt concentrations. The effect on the adsorption of (i) polyelectrolyte length, (ii) linear charge density of the polyelectrolyte, (iii) volume fraction of the polyelectrolyte, (iv) nonelectrostatic polyelectrolyte-surface interaction, and (v) surface potential or surface charge density, all at different salt concentrations and different surface conditions, was investigated. In most cases, as the salt concentration is increased, the adsorbed amount is reduced but the thickness of the adsorbed layer is increased. At low salt concentration and at constant surface charge density, the amount adsorbed is governed by the surface charge density through a polyelectrolyte-surface charge matching. At constant surface potential, a more diverse picture has emerged. A less regular distribution of the charges along the polyelectrolyte chain facilitates the adsorption.