This article is from the Depression FAQ, by Cynthia Frazier with numerous contributions by others.
There are several classes of antidepressants, all of which seem to work by increasing levels of certain neurotransmitters (most commonly serotonin, norepinephrine, and dopamine) in the brain. It is not entirely clear why increasing neurotransmitter levels should reduce the severity of a depression. One theory holds that the increased concentration of neurotransmitters causes changes in the brain's concentration of molecules, receptors, to which these transmitters bind. In some unknown way it is the changes in the receptors that are thought responsible for improvement.