Context
I was at a restaurant yesterday and one person on the table next to us was so loud that they sounded as if sat right at our own table, an annoying companion you could say.
Regularly, loud people are not too bothersome of an issue as to not being able to enjoy a meal, and you can even crack a joke at their expense, but this person was being rude to their own fellows, made me cringe from how she talked to one of them.
Even if that wasn't the case, sometimes the occasion calls for a more intimate or at least a slightly more comfortable and calm atmosphere.
Whenever I'm alone reading or writing or whatever and the restaurant is not that fancy, I move tables by myself taking the main things with me. I've noticed sometimes the waiters are very helpful and immediately start moving the rest of things, other times they sort of look like they're not sure how to handle the situation, I'm guessing it was because they have assigned tables and I moved to some area they're not responsible for? Additionally, having a company increases the complexity of that fórmula.
Question
What's the proper elegant way to do this without exhibiting I'm sort of a brutish man used to middle age pirate taverns?
Objective:
I'm looking for proper comprehensive procedure that covers manners, class, chivalry, spatial management (avoiding clumsy perception) and considers the sensibilities of the people I'm addressing without coming up as snobbish, that would be not only the waiter, but also and most specially my companions to avoid awkwardness and handle myself elegantly in a fancy setup or even sustaining a remarkable impression regardless of the setup being extremely fancy or not.