The biggest thing for me was learning, remembering, and using people's names. This may not be helpful for everyone (and that's okay), but it helped me be a more confident person in social situations.
Growing up I was painfully shy and awkward, but I had fantastic semantic memory and always did well on tests in school (does this sound like you?). One day, after I heard someone say "I'm terrible with names, sorry if I forget yours", I decided to heck with it! I'm going to be good with names! If I can memorize pi to however many digits, I can memorize that many names of human beings.
And it helped me :) People like it when you remember their name, and they like you more for using it. For me, unfamiliar things are scary, but knowing someone's name makes them a familiarity. Plus, there's a devilish part of me that delights in remembering someone's name who clearly doesn't remember mine. I always offer it easily, to not embarrass them. But it's a reminder that everyone's out here struggling to make connections just as much as I am - and I can handle it.
Ps: it's nice if you can let the person see you learn their name. It can feel creepy for a person to know your name without you telling them. If you learn someone's name without them telling you, all you gotta do is hit them with a "your name's Alex, right? Got it, thanks! I'm Daniel" and then you're covered