We have studied the effect of short-range interactions on polyelectrolyte adsorption at oppositely and similarly charged surfaces. The properties of the adsorbed layer, such as polymer surface coverage, layer thickness, and surface overcharging (for adsorption at oppositely charged surfaces), are calculated as a function of the surface charge density, the strength of the short-range interactions, and the ionic strength of the solution. The properties of dilute and semidilute two-dimensional adsorbed layers are calculated in the framework of the strongly correlated Wigner liquid model. In these regimes, the surface overcharging by adsorbed polyelectrolyte chains increases as a function of the square root of the salt concentration. At higher surface charge densities, when adsorbed polyelectrolytes form a three-dimensional adsorbed layer, we use the self-consistent mean-field theory to calculate the layer properties. Here, the polymer surface coverage shows nonmonotonic dependence on the salt concentration; it initially increases as the salt concentration increases at low ionic strengths and then decreases as the ionic strength becomes higher than some critical value. The decrease of the surface coverage at a higher salt concentration is due to additional screening of the surface charge by salt ions. We show that the adsorption of polyelectrolytes at similarly charged surfaces can only occur within the range of surface charge densities where the short-range interactions dominate the electrostatic repulsion between adsorbed chains and the charged surface. In these regimes, the salt dependence of the polymer surface coverage and layer thickness is similar to that for polyelectrolyte adsorption at oppositely charged surfaces that are dominated by short-range interactions.