Large networks of spiking neurons show abrupt changes in their collective dynamics resembling phase transitions studied in statistical physics. An example of this phenomenon is the transition from irregular, noise-driven dynamics to regular, self-sustained behavior observed in networks of integrate-and-fire neurons as the interaction strength between the neurons increases. In this work we show how a network of spiking neurons is able to self-organize toward a critical state for which the number of possible robust periods (dynamic range) is maximized. Self-organization occurs via synaptic dynamics. The resulting plasticity rule is defined locally so that global homeostasis near the critical state is achieved by local regulation of individual synapses.