"[b]"I can not work out ho
""I can not work out how it sends a signal with only 1 wire, surely there needs to be a circuit."
This system does complete a circuit only when a negative lead is connected to both the sending unit and the gauge..... (should also be grounded to any metal fuel tanks)..... AND if the sender lead (in your case, the green wire) runs up and to the fuel gauge "S" terminal without interruption.
This completes the circuit for a gauge reading...... providing that the sender/gauge are matched and are working!
However, the actual gauge is powered and also grounded at the helm....... and it reads only that resistance to ground via the sending unit (of which is also grounded)!
As Robert says, the sender's job is to create this variable potentiometer type resistance. The gauge knows how to interpret this resistance and uses this for the needle reading.
NOTE: The gauge must match in both polarity and in ohms resistance with any sender in order to work properly.
Rick ... aka Ricardo
28' SDN F/B w/ twin Volvo Penta 5.7L DP's