Detailed measurements of Hamamatsu R5912 photomultiplier signals are presented, including the single photoelectron charge response, waveform shape, nonlinearity, saturation, overshoot, oscillation, prepulsing, and afterpulsing. The results were used to build a detailed model of the PMT signal characteristics over a wide range of light intensities. Including the PMT model in simulated Daya Bay particle interactions shows no significant systematic effects that are detrimental to the experimental sensitivity.