Do not talk during a game, no explaining your moves, no telling your opponent to hurry up, no bragging to onlookers. Saying "check" is usually discouraged as well. The only things that you should be saying are things like draw offers, resignation, and such, and those should be said quietly.
To offer a draw, you have to make a move and say "I offer you a draw" on your turn and then press the clock, holding out your hand is improper as it pressures your opponent to accept your offer. I believe that the chess rules should introduce "draw chips" of some sort that can be placed in a designated spot next to the board to non-verbally offer a draw, but that is not in the rules.
Staying hydrated may be a good thing but there is a big drawback to drinking anything before or during a chess game.
You are allowed to not write your moves if you have less than 5 minutes on your clock (unless this event uses different rules).
Make sure that you get some practice with a 3D board, as playing online shifts the geometry even if you have played on a 3D board before, so it would be quite disorienting if you have not.
Writing down the moves can be tricky if you are not used to it, if possible use a board with coordinates around all four sides of the board.
Also, while online chess is often (not always) relatively rapid, over the board tournaments tend to use long time controls, sometimes several hours for a game. If you are not used to playing at such time controls it is easy to play too fast and to make bad moves. Remember that time that you have left over on your clock is time that you could have spent on thinking about your move.
Good luck in your tournament!