Chess clocks sit by the board, are set to the time limit for the game, and count down. Each player's time is independent; after you move you press a button and your clock stops and your opponent's starts.
https://en.wikipedia.org/wiki/Game_clock
[ Edited for grammar and readability. ]
In the USCF rules, not sure about FIDE, when it comes to Analog clocks, the style you are asking about, they get set so that the game ends, i.e. the flag falls, at 6:00. So, if you were playging a G/60, the clock would be set to 5:00 and if G/120 the 4:00, etc. It makes it easier to tell from across a room if the time is almost out.
I would have to look up the rules for multiple time control games though. That said, the standard now is a digital clock so fewer of the analogs will be seen in competitive play.
My question may be rather retarded but, why do chess clocks have to look like a clock on the wall? Are you supposed to set it according to the time of day before playing a game?