The fuel gauge is essentially a device for measuring current across a resistance. When the tank is full, the float for the fuel sender is raised (or should be) to its maximum height - and the resistor's effect is at its least. This current is measured by the fuel gauge, which should drop, as the fuel level (and float) lowers.
I'm no auto-electrician, but would suggest starting by checking the fuses, then the contacts at the fuel sender for any breaks or poor connections (this costs nothing to do, and is quite easy to check).
If that doesn't show any problem, then you may have to remove the sender unit - the float may have fallen off - thus the arm its attached to won't move from its lowered position. If this has happened, you will be looking at a new sender unit - which can be obtained second-hand.
Its quite straightforward to fit - just take the normal precautions with live electrical connections near fuel vapours.