Moving Coil Ammeters work in the principle that a coil passing a current in a magnetic field feels a torque that is proportional to the current when suspended as in the diagram of a moving coil ammeter below.
As the coil turns the hair spring exerts a restoring force that is proportional to the angle that is turned through. When these two forces balance, the coil stops.
The angular deflection of the coil is directly proportional to the current so the meter can be calibrated to read current.
Typically ammeters have very low resistances. This is desirable because the impact of the ammeter on the circuit is then minimized.