Going back to the OP's question, a lot of it is about acting, keeping a calm front and a cool head no matter what you are feeling like underneath. Putting on a front. And then you know you can do it, so you take confidence from that.
So what can you do about it?
Acting lessons or publc if you can afford them to learn that the show must go on no matter what you feel like, and to hold yourself well. Or something as part of a team.
Train the person to cope in any situation, ie take them out of their comfort zone, help them and then praise and reflect afterwards. As children we were made to hand round the eats at adult parties. None of this putting the children elsewhere to have a separate pizza gorge elsewhere in those days. So you had to talk to people.
Family meals with the extended family. You have to listen to granny going on again about her youth. And again not at the children's end of the table.
Two things to bear in mind
I'll do my best, no- one can ask for more
People take you at your own estimation.
And finally, most people love talking about themselves. If you appear interested in them, pleasant, not self absorbed, you will get a long way. Ignore yourself to focus in them. This is the one thing that imv Eton teaches brilliantly or did in my generation. They make you feel that your opinion counts.
None of this requires a private school education. At a school in which I am involved the staff often eat with the children. There are lunches with the governors. Tim Brighouse, the former London schools man and academic used to suggest that when going into a school you asked a child where they were going to go to university and preferably shook hands, even in primacy. Both unusual experience for some.