In a chess tournament, you are normally expected play with a chess clock. Don't worry if you don't have one; they're not required, just suggested. They keep track of how much time you have left to finish the game. If you run out of time, the chess clock will notify you with a visible signal, the game is over, and you lose.
Most scholastic tournaments play with G/45 time controls, which means each player has 45 minutes to finish the game. Adult tournaments often play at 40/2 SD/1, which means that each player starts with 2 hours to complete 40 moves, and then 'Sudden Death' 1 hour to finish the game. If you use up your 2 hours without completing your 40 moves, you lose. After you've completed 40 moves and have time left, it's proper to add an hour to both players' clocks to finish the game.
There are two kinds of clocks: mechanical and digital. A mechanical clock has a little 'flag', and when your time is almost gone, it starts to rise. As soon as you run out of time, the flag falls, and it is easy to tell that you have run out of time.
A digital clock will beep and flash when a player runs out of time. A digital clock is usually more expensive than a mechanical clock.