Chess clocks: timing games
The good news for newcomers is that you don't really have to worry about clocks. Many friendlies are played without clocks, and even in competition games you'll soon learn how to use them.
How clocks are used
Chess timers are two clocks connected together, and are designed so that only one of the clocks can run at any one time. Each player's thinking time is thus recorded on his side of the timer.
In competitive games, players have to make a certain number of moves within a certain time. Let's say that you each have to make all your moves in one hour, which will result in a game lasting a maximum of two hours. White's clock is started, and the time that he has left starts counting down. Once he has made his move, he presses the clock and his clock stops and Black's clock starts.
If a player runs out of time, the game is lost. This is immediate, and there is no appeal.
[In fact, there are closely specified exceptions to this rule; these come into play only on the rare occasions when someone has insufficient mating material left, or is playing on in a dead drawn position - but in all normal situations, if your clock goes then you lose the game].
The two types of clocks are shown above: there are analogue clocks, which are uncommon now in tournaments (but still used in many clubs); and on the right we see a digital clock. Clocks like these are more accurate and can be programmed with more settings. They are now standard in tournaments.
But as I said at the start, you don't need to worry too much about all this, as more experienced players will introduce you to the use of clocks.