How do i turn someone down, to hang out?

I feel that way too. Turning down a friend feels really bad, but it's better they understand than someone suffer in a social situation. I usually tell my friends that I'm not up for it. "Not my jam" is my first response, and my friends know me well enough to know that it means that I can't bring myself to go. Try to communicate. If someone asks you to do something you're not happy doing, say "no", shake your head, frown-give a clear signal. Telling someone to have fun always softens a rejection, as well as 'Take photos!' or something that shows that you care about the event (if you do), but don't want to go. Good luck!

Whatever you do, "I'll think about it" (similar, "I have to check what do i have to do that day") is a good reply, you have an immediate response but later you'll have an occasion to confirm you will not go with secondary means, like texting, that are less intimidating than face to face rejection handling. And, like a "No", if someone keeps insisting you can repeat yourself "Got it, as I said, I'll think about it", and change topic.

Be honest, if they know you have the valid reason of social anxiety to not hang out, they won't hate you for it. But people always know if you are making up reasons to not hang out, but they can't prove it so it just slowly damages relationships.