How do water meters work?

Your commonplace household water meter reads in cubic metres or cubic
feet, and most commonly displays your total consumption to the nearest
tenth, much like the odometer in your car measures total distance
traveled.
 
Basically, the pipe which supplies the water to your
house/apartment/domain has a flow meter at the entrance to your
property and meaures how much water has entered your house and records
that amount on a dial.

How does a water flowmeter work?
Your pipe's cirumferance is a known factor and the amount of water
flowing through that known circumference turns a 'paddle' or 'rudder'
that in turn rotate the meter's numerals that reflect the speed of the
'paddle's or 'rudder's rotations. This way the amount of water
supplied to your household is determined.

Most water meters do NOT require exteral power. The waterflow itelf
supplies the energy to record the amount of water consumed.


Your water bill will be determined depending on your family's or
household's consumption of water.

How does the water company or loacl authority know how much to bill you?

They either send a person to read your meter or determine your bill
based on your past average consumption.

A diagram of such a flowmeter can be found here:
http://cahe.nmsu.edu/pubs/_a/a-102.pdf


Sources:
http://www.markham.ca/markham/channels/waterworks/tipsinfo/meter.htm
http://cahe.nmsu.edu/pubs/_a/a-102.pdf

Very useful answer, many thanks