Congrats on your new ride! How new are you to riding in general? If you're otherwise comfortable riding and being on the road, riding in a casual group won't be that big of a deal to you.
A few do/don'ts: Ride predictably. Maintain a straight line and a steady pace. Don't do anything hurky jerky. Signal your intent using both hand and voice signals. Maintain adequate space between other riders, i.e., don't "tailgate." Signal for potholes and other road hazards for the riders behind you. Call out "car up," "car back, and "car around" as needed. Follow the rules of the road, even if others aren't.
I would introduce yourself to the others in the group as the opportunity arises. Some groups can be kind of reserved, so don't be shy about taking the lead. And have fun!
Live with intention. Walk to the edge. Listen hard. Practice wellness. Play with abandon. Laugh. Choose with no regret. Continue to learn. Appreciate your friends. Do what you love. Live as if this is all there is.
--Mary Anne Radmacher