We study the condensation of closed string tachyons as a time-dependent process. In particular, we study tachyons whose wave functions are either space-filling or localized in a compact space, and whose masses are small in string units; our analysis is otherwise general and does not depend on any specific model. Using world-sheet methods, we calculate the equations of motion for the coupled tachyon-dilaton system, and show that the tachyon follows geodesic motion with respect to the Zamolodchikov metric, subject to a force proportional to its beta function and friction proportional to the time derivative of the dilaton.