Fluorescence recovery after photobleaching (FRAP) is now widely used to investigate binding interactions in live cells. Although various idealized solutions have been identified for the reaction-diffusion equations that govern FRAP, there has been no comprehensive analysis or systematic approach to serve as a guide for extracting binding information from an arbitrary FRAP curve. Here we present a complete solution to the FRAP reaction-diffusion equations for either single or multiple independent binding interactions, and then relate our solution to the various idealized cases. This yields a coherent approach to extract binding information from FRAP data which we have applied to the question of transcription factor mobility in the nucleus. We show that within the nucleus, the glucocorticoid receptor is transiently bound to a single state, with each molecule binding on average 65 sites per second. This rapid sampling is likely to be important in finding a specific promoter target sequence. Further we show that this predominant binding state is not the nuclear matrix, as some studies have suggested. We illustrate how our analysis provides several self-consistency checks on a FRAP fit. We also define constraints on what can be estimated from FRAP data, show that diffusion should play a key role in many FRAP recoveries, and provide tools to test its contribution. Overall our approach establishes a more general framework to assess the role of diffusion, the number of binding states, and the binding constants underlying a FRAP recovery.