When learning another language how do you overcome the anxiety of talking to new people in the language you’re learning?

Practice speaking to one person you perhaps feel comfortable to at first. Gain skills and confidence by gradually branching out and trying to apply new vocabulary to specific situations

I know it’s scary in the beginning, but you really just have to do it! And of course there will be difficulties (finding words, a slight stutter), but believe me; the other person will just have respect for the fact that you’re trying to speak his/her language!
I’ve been in this situation several times (on both sides) and when listening to someone else speaking my language, I never thought they had to be afraid. I also proposed that if (!) they wanted help/corrections, I’d be happy to!
On the other side when I was trying to speak another language, I always informed them that I wasn’t 100% comfortable and asked if they could speak slowly and correct me.
And apart from that; do it A LOT! Listen to stories, watch movies, read books, have an online conversation (which gives you more time to think). Just do it and enjoy!

Remembering that people who speak your target language will be less likely to make fun of you for mistakes and help you. When a non native English speaker makes a mistake we hardly make fun of them. Instead we help and encourage.

Most people love talking to someone who is learning their language. It helps to remember that it is often enjoyable for people. It can be a reminder of teaching a child to speak and is fun!