The relationship between the transport of scalar properties and the statistics of material particle motion is examined. It is shown that evolution of the mean concentration field is determined by the statistics of single particles while two particle statistics describe the typical dispersal of individual property clouds. It is argued that oceanic observations of quasi-Lagrangian floats provide a useful and direct description of lateral advection and eddy dispersal. A simple model for predicting statistics of particle dispersal from Eulerian statistics of velocity is advanced. This model is tested against simulations of particle motion in random two-dimensional velocity fields with prescribed Eulerian statistics in which there is no mean velocity. The model is found to provide satisfactory description of the one and two particle statistics in statistically stationary, homogeneous, and joint normally distributed velocity fields. Adequately predicted are (i) mean particle velocity and mean square particle speed, (ii) the Lagrangian frequency spectrum of single particles from which the single particle diffusivity can be computed, and (iii) the mean square separation between particles from which the two particle diffusivity can be computed. A simple generalization of the theory to velocity fields with weakly inhomogeneous statistics describes the evolution of the single particle density, or equivalently the mean concentration field of a conserved scalar property, and describes particle migration induced by spatial variation of dispersion.