This is a tough question. There are many anti-anxiety drugs that can be prescribed by doctors, and this works for a lot of people. But one way is through meditation.
One can overcome anxiety by being taking anti-anxiety mediction prescribed by a psychiatrist, or engaging in talk therapy or cognitive therapy where you learn to control your own thoughts.
This often comes down to the personality of the individual. Most people, though, overcome it through simply putting themselves in the line of fire and dealing with it.
Anxiety can be debilitating but the easiest way to overcome it is to experience it without negative consequences. A trained therapist is the best way to get through anxiety.