I'm asking this question to provide players who are starting to play in tournaments a guide on proper behavior during games. I'll give an answer myself - perhaps we could supply an answer collectively via a community wiki.
First of all, be quiet and don't talk. You can whisper, but it is still considered rude / impolite.
If the round begins at 9AM, be there punctually. In some tournaments you might even lose the game if you're not there within the first 30 minutes.
If the game begins, you can say something like 'I wish us a good game', 'Good Game' and so on.
If something happens on the board and you don't know what to do, you can ask the referee or try to fix it with your opponent.
If there is a big chess game of two big chess players and you want to watch it, don't stand right next to them. Let them have their space. video
If you write your moves down on a piece of paper and you have to give it to the tournament administration, be aware that the result is the same on your slip + the opponent's slip. Both slips also have to be signed by both players.
No smart / cell phones are not allowed during your game (you need to turn them off) and it it also not allowed to turn them on if you watch some games, but you're not playing. The reason is, you could be cheating and some crap like that.
If you want, you can ask your opponent to analyze the game, after it is over.
If you have any further question, just ask.
When you are giving a Check, don't say it. Thanks Akavall
It's also considered poor behavior to eat at the board. Thanks Andrew Ng Of course, you can drink some water or something else, but be aware with the space. Normally the desks aren't that big.