Monte Carlo simulations are presented for the adsorption of a lattice-model isolated polyelectrolyte on an impenetrable, oppositely charged surface. We consider the effects of chain ionization, chain hydrophobicity, surface charge density, and solution ionic strength on the conformational and interfacial properties of the model system. The overall conformational properties of the model polyelectrolytes in the adsorbed state are similar to those of isolated polyelectrolytes in solution; however, the adsorbed chains are conformationally anisotropic. This anisotropy is described here by calculating the components of the polymer end-to-end distance in directions parallel and orthogonal to the interface. Detailed structural features of the adsorbed chains are described by the distributions of tails, trains, and loops. Tails are favored at low degrees of chain ionization, while trains become more favorable at high degrees of ionization. The number of adsorbed chain segments (e.g., degree of adsorption) increases with the surface charge density and decreases with increasing solution ionic strength; for some conditions, this degree of adsorption is a strong function of solution and surface properties.