I forced myself to do improv theatre. When I started, I was terrified, I was shy and doing that was definitely out of my comfort zone but the group I found was very welcoming and it quickly felt fun. The great thing about improv is that you learn to simulate different situations, you learn to be careful about your posture and mannerism as you take on different roles.
For someone who was as shy as I was, it was not easy to get started but I think it's the single thing that helped me the most.
Another commenter mentions toastmasters, I tried that but it really wasn't for me, some friends had great success with it though.
There's a book Improv Wisdom written by a former leader of Stanford's improv club that I found deeply insightful. I was looking into improv to address my social anxiety a while ago, sadly this was at the start of pandemic when everything shut down. Maybe I should go for it again.
If you like books, then “How to win friends and influence people” is great on this topic. The title is a poor choice. Don’t judge it by its title. It helps with shyness, among other things.
An also-effective approach is just to take the improv classes without ever performing on stage. That's all I did, but the lessons have stuck with me.
These days there seem to be more improv classes that are friendly to that, just people who like playing with one another. So if people are scared even by the classes, I'd suggest asking the instructor for something that's very beginner-friendly and not totally oriented on performance.
For someone who was as shy as I was, it was not easy to get started but I think it's the single thing that helped me the most.
Another commenter mentions toastmasters, I tried that but it really wasn't for me, some friends had great success with it though.