We investigate by lattice Monte Carlo simulation the kinetics of adsorption of isolated linear homopolymers onto a flat surface with a strong, short-ranged attraction for the segments. We focus on limiting cases corresponding to strong physisorption and chemisorption. initially, the polymer has a conformation representative of the bulk (dilute) solution, but with a few peripheral segments in contact with the surface. Subsequent adsorption is tracked by monitoring a number of mechanical variables. By averaging over initial configurations, and over appropriately selected time windows along individual trajectories, we determine the adsorption kinetics and find the effects of chain length and segment/surface interactions on the characteristic time for adsorption, tau(ads). For all situations investigated, tau(ads) increases algebraically with the number of segments N; i.e., tau(ads) similar to N-alpha, with alpha being considerably smaller than that for scaling of the bulk relaxation time of the chain, tau(R). We find that alpha depends on the details of the short-ranged surface/segment interaction potential. The results are rationalized with scaling-level analysis.