We perform kinetic Monte Carlo simulations to examine the kinetic properties of one-atom-high islands formed by atoms adsorbed on a single-crystal surface. At sufficiently high temperature, the atoms can leave the island to migrate on the substrate. We call this process evaporation. We find that most of the evaporation events are described by a Poisson process characterized by a rate constant k(N, T), where N is the number of atoms in the island and T is the temperature. We also observe correlated evaporation events, which tend to follow each other in rapid succession. This complicated situation can be described, however, by an effective Poisson process that is defined to generate the correct vapor pressure. The dependence of k( N, T) on N follows an equation proposed by Metiu and Rosenfeld, and not a power law observed in previous work. The random motion of the atoms around the border of the island causes its center of mass to move along the surface. This island motion is diffusional, except at the shortest times. The dependence of the diffusion coefficient on N is a power law (if the smallest islands are excluded). The exponent is not universal and depends on temperature and the parameters of the model. Theory predicts universal behavior for very large islands and we assume that in our simulations we have not reached this regime.