A new learning rule (Precise-Spike-Driven (PSD) Synaptic Plasticity) is proposed for processing and memorizing spatiotemporal patterns. PSD is a supervised learning rule that is analytically derived from the traditional Widrow-Hoff rule and can be used to train neurons to associate an input spatiotemporal spike pattern with a desired spike train. Synaptic adaptation is driven by the error between the desired and the actual output spikes, with positive errors causing long-term potentiation and negative errors causing long-term depression. The amount of modification is proportional to an eligibility trace that is triggered by afferent spikes. The PSD rule is both computationally efficient and biologically plausible. The properties of this learning rule are investigated extensively through experimental simulations, including its learning performance, its generality to different neuron models, its robustness against noisy conditions, its memory capacity, and the effects of its learning parameters. Experimental results show that the PSD rule is capable of spatiotemporal pattern classification, and can even outperform a well studied benchmark algorithm with the proposed relative confidence criterion. The PSD rule is further validated on a practical example of an optical character recognition problem. The results again show that it can achieve a good recognition performance with a proper encoding. Finally, a detailed discussion is provided about the PSD rule and several related algorithms including tempotron, SPAN, Chronotron and ReSuMe.