Look at the board below. Black is in check from a bishop standing six squares away on a2, and in a tournament nobody is going to mention it. No arbiter, no opponent, no rule. Miss it and you will play an illegal move, and then you have a problem.
7 
g The Laws never ask you to say it
There is no article in the FIDE Laws of Chess that requires a player to announce check. Not one. Check is defined by the position, not by anything anybody says: your king is attacked, and you have to deal with it on your next move. Whether the words were spoken makes no difference to whether you were in check.
School chess clubs and family house rules are where the idea comes from, helped along by every game of chess ever filmed, in which somebody always says it. So people turn up to their first tournament expecting the announcement. They are surprised twice: nobody says check, and nobody says anything at all for four hours.
In a tournament, keep quiet
Announcing check in a rated game is at best pointless and at worst a penalty. Art. 11.5 says it is forbidden to distract or annoy your opponent in any manner whatsoever, and a room of eighty players in the fifth hour of a game does not need commentary. If you say it repeatedly after being asked to stop, an arbiter can treat it as exactly that, and what happens when you talk during a game sets out where the line sits.
There is a less high-minded reason too: a player who announces check is doing the opponent’s work for them.
Online the question does not arise: the interface refuses illegal moves, and many boards flash the king in red, which is one reason players who learn online find their first over-the-board game so unnerving. Nothing helps you there.
When the check goes unnoticed
Say your opponent misses it and picks up a rook on the other side of the board. What happens next depends on where you are.
At home, tell them, take the move back, let them find a legal reply. You never capture the king, in any setting: the king is never taken, and grabbing it to prove a point is an illegal move of your own.
In a standard-play tournament, stop the clock and call the arbiter. The position goes back to before the illegal move, the offender’s opponent gets two minutes added, and a second illegal move by the same player loses the game. The full procedure is on an illegal move in a tournament, and what it means for the game if the check slips through unnoticed for several moves is covered on what if you do not notice check.
Say it at home if you want to
With a seven-year-old, say check. Say it loudly. They need to hear the word attached to the shape on the board about fifty times before they see it on their own, and there is no prize for silence in your kitchen.
The habit to build instead of listening for the word is a four-second scan before every move: the four lines out from your king (two diagonals, the file, the rank), then the eight knight squares around it. Mate-in-one puzzles drill the same scan from the attacking side, since every one of them hides a check that nobody is going to announce. Do it every move and nobody will ever need to tell you.