To check a tank level gauge, you must first gain access to it, which may require removing the instrument panel. Once you have access to the fuel gauge's wiring, connect the back of the fuel gauge to the ignition switch with a jumper cable, and turn the ignition on.
If the gauge starts to work, it means the wiring between the gauge and ignition switch is bad. Replace the defective wiring.
If that doesn't work, attach one end of the jumper wire to the gauge's ground terminal, then attach the other end to any bare metal on the vehicle's frame. If the fuel gauge starts to function, the fuel gauge grounding wire is defective and must be replaced.