Extinction refers to the cease of activity that results as a consequence of a stimulus, or a condition.
As part of our natural psychology, specific human and animal reactions occur as a result of a stimulus. We react to everything that we see, hear, taste, smell or feel. When the reactions come as a result of a specific sight, sound, taste, scent, or physical touch, we call that a classical conditioning response. This is because a stimulus that is conditioned (say, the scent of fresh-made spaghetti), may immediately trigger the myriad of neural connections that trigger the hormones that cause hunger. If this hunger occurs each and every time we smell spaghetti, then we have been classically conditioned (conditioned stimulus- spaghetti + unconditioned stimulus- sense of smell= the feeling of hunger.
In order to extinguish a behavior in Pavlovian classical conditioning, the best way to do so is by understanding where the reaction is coming from and thus avoiding altogether any contact with the causative agent that triggers the behavior. In alcoholics, for example, many unconditioned and conditioned responses have collaborated to develop a social need to consume alcohol. Hence, half-way homes, hospitals, and support groups are put together to remove the stimulus altogether and thus create a habit of not drinking by eliminating the factors that motivate it.
Skinner's Operant Conditioning is a process in which we recognize the signs of classical conditioning but put a plan of action into play to manipulate the conditioned stimulus in order to 1) reward, 2) punish, or 3) remove the stimulus (without punishment).
Operant conditioning is done at intervals with the aim of rewarding an expected behavior each time it happens. The extinction of a behavior through operant conditioning is expected to occur through a schedule of reinforcement that may keep the behavior at bay.
It is like reverse psychology: when a student is being rowdy and mean, the best course of action is for the teacher to reward the good behaviors daily, so that the negative behavior becomes extinct. At first, the positive reward is done immediately to ensure the student that the behavior is being moderated. Then, a partial schedule is given where the student will continue to be rewarded at longer intervals. As the student finds other ways to obtain reward from good conduct (less problems at home, making more friends, not going to the Principal's office, a better feeling of self-esteem)the bad behavior will likely become extinct. However, a good plan of operation has to be in place and there has to be a commitment to consistency in the manner in which the rewards will be provided.