There is extensive evidence that biological neural networks encode information in the precise timing of the spikes generated and transmitted by neurons, which offers several advantages over rate-based codes. Here we adopt a vector space formulation of spike train sequences and introduce a new liquid state machine (LSM) network architecture and a new forward orthogonal regression algorithm to learn an input-output signal mapping or to decode the brain activity. The proposed algorithm uses precise spike timing to select the presynaptic neurons relevant to each learning task. We show that using precise spike timing to train the LSM and selecting the readout presynaptic neurons leads to a significant increase in performance on binary classification tasks, in decoding neural activity from multielectrode array recordings, as well as in a speech recognition task, compared with what is achieved using the standard architecture and training methods.