Knowing what anxiety is and where it comes from is a good start. Anxiety is a natural feeling that comes from our primitive brain to be on alert for danger. It is the "pre" fight flight or freeze. Think trying to forage for food while there is rustling and you know that sabertooth tigers are in the area. It is an experience of hyperarousal at ones surroundings and has it's use, like being anxious using a new saw will help you see and recognize all the dangers early on. The problem becomes when the anxiety isn't experienced, it grows worse as the brain didn't get the answers it was looking for.
For example, you enter a room full of new people and feel a little anxious, that is normal. You might notice where the exits are for example. If you experience the anxiety, it will pass. Usually walking around the room and noticing people, probably seeing random little details, and generally just surviving the sabertooth tiger.
Now the next time you enter that same room you will not feel as anxious. Your brain remembers that it has been here before and successfully foraged and as such doesn't ramp up all the chemicals that make the anxious feeling.
If you had avoided the room however and left you would now feel more anxiety the second time you went. By not experiencing it the first time you effectively told your brain that you experienced danger and needed to flee the tiger. You literally made one of the post anxiety choices (flight) and this told your brain that it was right to be extra observational because there was danger.
This chart helps show how that short term avoidance creates a long term anxiety:
So how can you experience anxiety instead of avoiding it when your cycle is already too big? Well, anxiety is a physical state as well, and just like the mental state will induce the physical, the physical will induce the mental.
While sitting in a chair clasp your hands together. Look at the fingers and observe which way they interlock. It feels comfortable. Now unclasp them and reclasp them backwards (if your left pointer was on top, now make it your right pointer). You should actually feel your body start to induce an anxious state. E36 M3 with it and observe your body and it's feelings. Do your hands tingle? Are you sweating? Do you feel a nervous tick, a restless leg, or the desire to leave? That's all good, that's anxiety!
Continue the clasp until those feelings start to subside. That's your brain recognizing that there is no danger in this new situation and making the chemical and physical changes to come down from hyperarousal. If the hand clasping doesn't induce it, try crossing your legs backwards.
Successfully experiencing anxiety without the flight choice will start to retain your brain that anxiety doesn't always mean danger and you can start to experience it successfully in other areas. That's what "working through it" really means, going to hyperarousal, recognizing no danger, and continuing to stay in the situation until it becomes comfortable (regular arousal).