The strength of many synapses is modified by various use and time-dependent processes, including facilitation and depression. A general description of synaptic transfer characteristics must account for the history-dependence of synaptic efficacy and should be able to predict the postsynaptic response to any temporal pattern of presynaptic activity. To generate such a description, we use an approach similar to the decoding method used to reconstruct a sensory input from a neuronal firing pattern. Specifically, a mathematical fit of the postsynaptic response to an isolated action potential is multiplied by an amplitude factor that depends on a time-dependent function summed over all previous presynaptic spikes. The amplitude factor is, in general, a nonlinear function of this sum. Approximate forms of the time-dependent function and the nonlinearity are extracted from the data, and then both functions are constructed more precisely by a learning algorithm. This approach, which should be applicable to a wide variety of synapses, is applied here to several crustacean neuromuscular junctions. After training on data from random spike sequences, the method predicts the postsynaptic response to an arbitrary train of presynaptic action potentials. Using a model synapse, we relate the functions used in the fit to underlying biophysical processes. Fitting different neuromuscular junctions allows us to compare their responses to sequences of action potentials and to contrast the time course and degree of facilitation or depression that they exhibit.