I don't tend to avoid anxiety-producing things, I engage them head on. Here's how I did it.
I was forced to take a speech class in uni, I got it out of the way in my first year, and it was the best class I took that year!
I took a serious look at how I viewed the world, which was really messed up. I was assuming people were thinking bad things about me, or laughing at me. But I had no evidence for that. So I stopped the "stinking thinking" and started thinking about other reasons people were laughing. Well, I'm a funny guy, I make jokes on purpose. The people weren't trying to be mean to me, sometimes my mistakes WERE funny! So I had to reprogram my bad habits by not thinking the worst all the time. This took me years and I still work on it.
2 years later, still in Uni I took a big risk with a job at a Fortune 500 company. My pay was more than minimum wage, and I learned a lot. I needed the money for college. Then towards the end of the summer I learned I had to make a presentation to a room full of Vice Presidents! I practiced my presentation for at least 2 weeks and when I went there, all the VPs were very nice. One even asked if he could get ME a coffee! I was stunned. I was learning all my assumptions about people were wrong, or at least over generalized.
All during college I addressed my social anxiety and practiced small talk. I went out to parties. I got invited to a lot of parties but I'm not really a party person. But I decided to go. I would start going for about 30 minutes at first, long enough to challenge me but not too long to make me sick of the whole experience. Do not over do this, but challenge yourself.
Gradually, with more practice, I got better at small talk. You can get better at just about anything with practice.
Around this point in my life I started to look back at my life and noticed how my friends and peers were trying to help me with my anxiety in their own awkward way. It didn't matter that they didn't do a great job, what mattered was they TRIED, because they CARED. They really cared. I was stunned at looking at these things again, my negative assumptions about the world continued to crumble.
I no longer struggle with social anxiety, but I'm not a big talker either. I'm fine being in social situations, because I challenged myself to meet a goal, and I didn't beat up myself when I had a bad day and just wasn't feeling great at a party and failed at small talk. I might leave that party, but I didn't give up... I went to another party the next day.
As another example, I'm a bit afraid of heights. So I went on an obstacle course about 2-3 stories up in the trees. Some obstacles were zip lines, and I did zip lines over an alligator park, over the alligator pens. What a workout, but what a rush! It was tiring and fun all at the same time!
Now I'm terrified of tarantulas, so to address that I might find a pet show or pet shop and ask to hold a tarantula.
All this takes years to do. Take baby steps, don't take too big a step at once. Don't put yourself down. Once I started conquering fears, progress started to speed up. Life isn't perfect, but it does get better!