Dogs that suffer from anxiety disorders tend to be abnormally afraid of certain stimuli, like noises or objects, or experiences, like having their owner leave home. This over sensitivity expresses itself as panic and aggressive and / or destructive behaviors.
Desensitization is the process of very gradually exposing an animal to the stimulus or situation which they are extremely afraid of. By slowly and safely exposing the animal to their fearful stimuli, the theory is that the fear will slowly lessen, until they no longer react with panic. For example, for noise phobias, audio recordings of thunderstorms and other fearful noises can be played and gradually increased in volume after each successful session. For separation anxiety, starting with short absences and gradually increasing the length of time away from the home can work.
Desensitization needs to be done in a formal manner - with regular, monitored sessions. Some studies suggest that long desensitization sessions (30 - 45 minutes) can be more effective than multiple short sessions. And it can take weeks, or months, to determine if it has been effective. For help with desensitization, it is recommended that a pet owner find a Certified Applied Animal Behaviorist (CAAB or ACAAB) or a board-certified veterinary behaviorist (Dip ACVB).
The theory behind behavioral desensitization is actually analogous to the proven success of allergy immunotherapy (allergy shots). Just as injections of small amounts of specific allergens causes the body to develop immunity to those allergens, gradual, controlled exposure to fearful stimuli can keep the nervous system from over-producing the hormones and neurochemicals which cause panic.