A float chamber works by allowing liquid within the chamber to lift a float which is attached by some means to a valve which allows in more liquid. When the level is low, the float drops and opens the valve, allowing in liquid until the float rises sufficiently to close off the valve again. This is identical in principle to the ballcock valve.
One drawback of the basic type of float chamber described is that it only operates correctly when it is the right way up, so more sophisticated solutions are needed in aircraft.