We present results from a series of molecular dynamics simulations for adsorption and spreading of polymer chains onto a flat surface. We consider both homopolymer chains and "protein-like" copolymer chains in the simulations. For homopolymer chains, we have considered both good and poor solvent conditions, and for copolymer chains, we have considered several conformations of the non-adsorbing monomers. Our results indicate that when the adsorption strength is strong enough, a scaling description of the adsorption kinetics works well for homopolymers in both good and poor solvent conditions. When the adsorption strength is not strong enough, the chains adsorb partially, and one needs to consider effects of this partial adsorption in the scaling description. For each of the three primary structures of the copolymers considered in this study, the polymer chain does get adsorbed to the surface but the kinetics of the adsorption process depends on the specific structures of the copolymer chains.