How do you get over your longstanding phobias?

Desensitization. Systematic desensitization is a technique where a person creates a heirarchy of their fears or phobias. Then a psychotherapist helps the person learn relaxation techniques. Then the psychotherapist exposes the person to the fears or phobias in vitro (in a lab) or in vivo (real life). This process can help a person overcome phobias.
CBT. Seek a cognitive-behavioral therapist who specializes in phobias. One method they use is systematic desensitization which slowly and incrementally brings the person closer and closer to the thing they are afraid of in slow, graduated steps that help make the anxiety more tolerable.