Controlled burns serve numerous purposes. Generally speaking, they don't help the trees as much as the diversity of plants in the forest bed. Left undisturbed, some plants in the undergrowth tend to dominate, blocking growth of the less dominant plants. Burns will reduce the dominant plants, thereby creating more diversity among the plants, which leads to more diversity among forest animals, due to increased variety of foods and habitat. They can also be used to reduce proliferation of forest pests, such as ticks, chiggers, as well as other insects that are destructive to the trees.
Reduction of "natural fuels" - fallen timber, dead trees, limbs, grasses, etc - has become an increasingly important reason to conduct controlled burns, as people continue to build neighborhoods within forest areas. While these natural fuels don't necessarily increase the number of forest fires, they increase the severity of fires, since the dead timber and high grasses burns with more intensity than live trees. Eliminating this fuel under controlled conditions is much better than leaving it to burn during natural forest fires.
The forest service uses a number of tools to conduct controlled burns, primarily knowledge.

Time of year, temperature and humidity, seasonal wind patterns can all play a factor in when and how to burn. In some cases, bulldozers and chainsaws can be used to clear fire breaks prior to a burn, in order to contain areas of the burn.
http://www.clemson.edu/psapublishing...ry/forlf30.pdf