A good chess player can spend hours thinking about one move. That's why they invented the chess clock. To limit the amount of time a player can think so the chess tournament can stay on schedule.
Most kids play too fast, and that's why most kids don't need a chess clock.
Most tournament directors have a few extra chess clocks, and will place a chess clock on a game that is taking too long.
The player who is using the clock for the first time really has to remember one thing: to remember to press the clock after the move is completed.
The "Same Hand" Rule: If a player moves a piece with the left hand, he must hit the clock with the left hand. If a player makes a move with the right hand, the player must hit the clock with the right hand. It just has to be the same hand, per move. And if a player violates this rule by accident, it's not a big deal. The player might receive a friendly warning or the experienced player might just not say anything.
Notation Penalties: A player who does not notate is breaking USCF rules. Tournament directors may subtract 5 minutes from a player that does not notate. This is common practice in scholastic tournaments. This rule is usually used with beginners.
This Same Hand rule serves a very good purpose - to make sure that a player doesn't accidentally press the clock BEFORE the move is made. That would be unfair. Imagine a player who has one hand over a clock button and the opposite hand holding a piece and making the move. This player will often accidentally press the clock too early. The opponent will have to "worry" about what came first, the move or the clock press. By using the Same Hand rule, no one accidentally hits the clock first.
Also here's another tip: Use your HAND to press the clock. Sometimes you will players hit the clock button with a chess piece. Using a piece to press the clock button damages wooden pieces and damages clocks. The USCF used specific wording in their rulebook saying that a player must press the clock using a hand. The clock company Chronos designed a clock that will only react to the human touch, and not the touch of the pencil. Basically too many people break pieces and clocks by hitting them with chess pieces.
The most important thing for kids to remember is: stay calm when the clock is placed on your game. The tournament director is probably giving you PLENTY of time.
This is just an estimate, but at the time of writing this article, I have seen maybe 100,000 rated games played with clocks, and I've seen maybe less than 20 people lose on time.
Time Delay: Modern digital chess clocks have a 5 second time delay. The United States Chess Federation encourages all players to use this feature. It basically means that if you make your move in under 5 seconds, you lose no time. Because of this time delay, it is very hard to lose on time.