Spiking neural network is a type of artificial neural network in which neurons communicate between each other with spikes. Spikes are identical Boolean events characterized by the time of their arrival. A spiking neuron has internal dynamics and responds to the history of inputs as opposed to the current inputs only. Because of such properties a spiking neural network has rich intrinsic capabilities to process spatiotemporal data. However, because the spikes are discontinuous 'yes or no' events, it is not trivial to apply traditional training procedures such as gradient descend to the spiking neurons. In this thesis we propose to use stochastic spiking neuron models in which probability of a spiking output is a continuous function of parameters. We formulate several learning tasks as minimization of certain information-theoretic cost functions that use spiking output probability distributions. We develop a generalized description of the stochastic spiking neuron and a new spiking neuron model that allows to flexibly process rich spatiotemporal data. We formulate and derive learning rules for the following tasks: - a supervised learning task of detecting a spatiotemporal pattern as a minimization of the negative log-likelihood (the surprisal) of the neuron's output - an unsupervised learning task of increasing the stability of neurons output as a minimization of the entropy - a reinforcement learning task of controlling an agent as a modulated optimization of filtered surprisal of the neuron's output. We test the derived learning rules in several experiments such as spatiotemporal pattern detection, spatiotemporal data storing and recall with autoassociative memory, combination of supervised and unsupervised learning to speed up the learning process, adaptive control of simple virtual agents in changing environments.