Small steps.

If you throw yourself into the deep end right off the bat you will just flood yourself and dread having to do it the next time.

You need to ease into it slowly, in manageable amounts, and stop once you've reached your limit. That is how you build up the resilience that will allow you to experience less anxiety... positive experiences.

So say you're anxious about going to the mall alone. Maybe you'll start out just going to the parking lot then leaving. Or walking through the mall and out, not shopping. Then the next step would be to look around a little, then buy one small thing. The point is to take very small steps. Each time it becomes less scary, until finally you can do it without experiencing the anxiety you originally had, even as you do more than you originally thought possible.