Pruning should be done in the winter, just before new growth begins to appear in the spring. If the tree is newly planted, prune it to an open-centered shape. If it is more established, prune away all but four evenly spaced branches which serve as the tree's primary scaffold branches.
After the tree is done producing fruit for the year, examine the plant and prune away branches that are undesirable, including those that are at acute angles to the trunk and those that are too close to the primary scaffold branches.
If suckers start growing on the fig tree, use a shovel to remove them from the base of the tree as they appear. Whenever you notice damaged or diseased wood, including broken branches, remove them; make the cut about 6 inches into the healthy wood, if possible.