I’m a bit socially anxious myself. I’ll echo some of the above. The new player briefings are great, definitely go to one you’ll pick up loads of tips and tricks, and you’ll also get to meet your nation’s egregores. I’d also say check out the public speaking workshop that’s held at 1pm in the military council tent on the Friday, I’ve found its a good way to loosen up before the game starts.
I tend to struggle a bit with the shear volume of in character info on the field, reading the winds of war/fortune before the event really helps with some talking points. Also visit some teahouses. Teahouses are generally quite relaxed (well at least mine is), the proprietor will usually chat to you, which I find helps me come out of my shell a bit. They’re also good sources of ic gossip, which you can spread around Anvil to your heart’s content.
Another thing is people will look busy, constantly running around the place. Don’t be afraid to flag someone down to ask them something. I know it’s easier said than done, I struggle a bit with it myself. Just use the magic phrase “I’m new to Anvil” and they will stop and help you.
Use your egregores. They are there to help and to make sure you’re not miserable. Don’t be afraid to ask them for advice.
Don’t worry too much about dropping out of character. I think most of us do it from time to time. Also don’t worry about taking too long to respond to something, improvisation takes practice and we were all new once. I’m not great at it, but I’m finding I improve everytime I set foot on the field.