The car's fuel indicator doesn't work

This could be a fault with the gauge or the sending unit and costing would depend on what is wrong. Remove the rear seat cushion and unplug the connector of the fuel pump and sending unit. Turn ignition on and if the gauge needle drops to the lowest position turn ignition switch off. Reconnect the wire harness and turn ignition switch on again. If needle goes to initial position, the sending unit is stuck (unless the fuel is at that level which means it is showing correctly) or you have a bad ground circuit.

To test the low fuel level warning light, with the wire connector at sending unit disconnected, use a test light to ground the Green/Yellow wire, turn ignition switch on. If the light indicates, it would mean a fault with the sensor in-tank or a poor ground circuit. Btw if the fuel level is faulty, the fuel level might not have dropped low enough for it to come on.
If light does not indicate with above procedure, the illumination bulb could be bad or there is a fault with the wiring circuit.