I don't know if you ever can truly overcome social anxiety, but it certainly can be managed.
People who tend to relate to their social anxiety in terms of a disease or externally applied condition seem to fare better than those who identify with it and make it a part of their identity: "I have social anxiety" versus "I am socially anxious". Social anxiety is not a personality, the commonalities between sufferers do not extend beyond the condition. *
The other major factor, I feel, is access to a novel environment. I believe that it is absurd to expect changed behavior to emerge from old environments. That's not how conditioning works. If you want to recondition yourself, one of the best ways is to put yourself in situations with novel stimuli. Moving away from home, going on a road trip, camping, etc. The key is that you be around people in an environment where your behaviors have not had time to become ingrained, freeing you to experiment with other ways of being.
Another one, which probably is rarely mentioned and perhaps frowned upon... but I will mention because it can be effective... is psychedelics. It is my experience that strategic, intelligent use of psilocybin and LSD in the right environment can help with reconditioning people's behavior. It has a tendency to give you a perspective that is, more or less, free of social constructs, which allows you to sort reasonable and unreasonable beliefs in a tangible way. They also utilize neural pathways that are often unused, allowing for a reconstruction of behavior through the exercise of fresh pathways.
Therapy is the last major one that I can identify. It speaks for itself and really can be an effective stepping-stone if you get a good counselor/psychologist/psychiatrist.
.. probably a certain acceptance of discomfort... as you will have to continuously push yourself into uncomfortable situations to improve.
becoming competent and thereby confident in abilities that you see as valuable...
Since the body is a unified whole, there is no real distinction between your mind and your body, as the body and brain are one system. So, a strong, healthy body is the absolute foundation of good mental health. If I had to organize this post as a list descending by importance, this would be first. You also will build confidence when you realize that you owe it to yourself to be healthy.