Dead, damaged, and diseased branches should be removed as soon as possible. Otherwise, the best time to prune is in late winter, early spring, just before the tree begins to open its buds. Some trees, such as maple and dogwood, will bleed sap at this time of year. This bleeding should not harm them.
While pruning can be done anytime, it is always good to avoid hot dry periods and extreme winter cold. If you do prune trees after the leaves have opened, be sure to allow them to fully develop their leaves plus some additional time to recoup the energy they used.