The quietest room I have ever stood in had two hundred people in it. Round five of a weekend open, eighty boards, and the loudest sound was a clock being pressed three tables away. Tournament chess is a silent game, and the small number of things you are allowed to say fit on one hand.
The whole list
Say j’adoube, or I adjust, in your own time and before your fingers arrive, if you want to centre a piece that is sitting across two squares. There is a page on that one word, because saying it afterwards is worth nothing.
Say I offer a draw, once, after you have made your move and before you press the clock. That is the moment the Laws set aside for it, and how to offer a draw covers the etiquette around it.
Say I resign, or stop the clock and hold out your hand.
Say arbiter, with your hand up, having stopped the clocks.
You may also say check. It is allowed and it is not required, and most players above beginner level do not bother.
That is it. Everything else is conversation with somebody who is trying to calculate a four-move line.
Distraction is the actual rule
Art. 11.5 is short and very broad: it is forbidden to distract or annoy the opponent in any manner whatsoever, and it names unreasonable claims, unreasonable draw offers and introducing a source of noise into the playing area as examples.
In practice that covers asking are you sure about that, sighing at your own move, humming, tapping the table, kicking a chair leg, standing behind your opponent’s chair while they think, and offering a draw for the fourth time in ten moves. Penalties come from the ladder in Art. 12.9, and the first rung is a warning. The second is time on your opponent’s clock.
No notes, no advice, no second board
Art. 11.3.1 bans notes, sources of information and advice during play, and bans analysing a game on another chessboard. So the opening file in your bag stays in your bag, you do not ask your coach anything in the corridor between moves, and you do not wander over to a spare set and try out a line. Looking at other games in the hall is fine. Setting one up is not.
Electronics are stricter still. Under Art. 11.3.2 a phone on your person in the playing venue can cost you the game, and arbiters at big events do enforce it.
The silence is doing you a favour
Every sentence you say at the board gives something away: that you are happy, that you are worried, that you have seen something. Strong players give away nothing, and their faces are the same at move twenty and at mate in two.
There is also a practical use for all that quiet. The half a minute you are not spending on small talk is the half minute you should spend asking what your opponent’s last move actually attacked, which is the habit that stops most blunders before they reach the board.