The seasonal succession of plankton species has long fascinated aquatic ecologists. Despite this interest, there has been a limited number of mathematical models of seasonal succession, likely due to the paucity of analytical tools for studying nonequilibrium dynamics. Here we present a new approach to modeling the dynamics of forced food webs. Assuming that species growth is fast relative to the period of the forcing, seasonal succession can be thought of as a series of transitions between different community states. Our techniques allow for the calculation of the timing of these transitions and predict which pathways will be followed, facilitating fast numerical simulation of the process as well as some analytical results. We illustrate these techniques on the "diamond food web", which can result in a wide variety of successional patterns and nonlinear dynamics.