How is the bus ticket system operated? I mean how the bus people come to know where one has taken the bus?

Not sure about the US but in the UK the driver changes the stage numbers as he proceeds along his route, the stage number , where you got on, is stamped on the ticket along with your destination, class of ticket (single journey or return) cost of journey, vehicle number, driver number, time ticket issued and ticket number. There is usually 3 or 4 stops between stages but you will always be charged from the stage before you're stop if the stop was not the stage. A stage is where you have a price change, the further you travel the more stages you pass and the more you pay.

As the other person was mentioning, it's marked on the ticket. However, whether the person gets off is really on the honour system unless they give the driver a hassle about the fare or are otherwise a nuisance. In larger cities like London, you pay the fare per bus rather than per distance.