How is addictive personality disorder treated?

With care. "addictive personality disorder" does not exist in the dsm-iv. But addiction itself is best treated in a comprehensive program involving mental, physical, emotional, and spiritual care. Some personality patterns may lead to difficulty, which can be dealt with in personal therapy. 12-step programs are also helpful in addressing common issues. The whole program is much larger than this, though.
Psychotherapy. All personality disorders are long standing character traits that interfere with interpersonal functioning. The best course of treatment is long term psychotherapy with someone experienced in the treatment of personality disorders. Group therapy may also be beneficial as it provides the opportunity to get real time feedback from peers under the leadership of a skilled facilitator.