We explore the physics of protoplanetary disk evolution in the presence of a photoevaporative wind. We construct analytical models that demonstrate the effects of disk wind loss and apply these models to the dispersal of disks around T Tauri stars. In particular, by calculating and analyzing the Green's function that characterizes the effects of the wind on the disk structure, we can understand the competing effects of viscous accretion and disk mass loss. In agreement with published disk evolutionary simulations, we find that inner disk holes can develop if the ionizing luminosity responsible for the photoevaporative wind is maintained at sufficiently high levels and that if the source of photoionizing photons is dominated by the star-disk boundary layer, the photoevaporative mass-loss rate decreases to a much smaller value. We derive analytical estimates for the mass-loss rates and disk dispersal times in these two regimes. In general, photoevaporative wind loss is inefficient in T Tauri systems. In all disk wind models considered, the photoevaporative wind is able to remove only a mass comparable to the mass of Jupiter.