In spite of what you see around town, the less you can prune citrus, the better. In nature, they want to be a shrub, they only take shape of a tree when we prune them to do so. It is best to limit pruning to remove dead or damaged wood and branches that may be taking away from the overall appearance of the tree. Pruning should be done to remove water sprouts (very thin or waxy looking branching) or suckers, or to remove any frost damaged material from the tree. Prune to keep trees healthy, attractive and within bounds. Other than lemon trees, citrus trees do not require frequent pruning to remain productive.
Remove branches that grow inward, in order to give the citrus tree a well groomed appearance. Tree trunk paint or a product called Go Natural Paint to the trunk, can be applied to exposed bark areas which will protect the thin bark from the strong U.V. rays in Arizona sun. You can also wrap in burlap cloth as an alternative.
Do not prune citrus trees in the fall. Doing so can encourage a growth spurt which will only be frozen a short time later in winter months. Not that we have a lot of hard freezes in the desert climate where we grow citrus, but it's doesn't take much especially on tender new growth.