Alright then. Nearly all tank senders are potentiometers acting as variable resistors, meaning they change the resistance in the sending wire as the fuel level varies. The gauge circuitry reads this and moves the needle proportionally. To confirm that's working properly get your multimeter out and remove the sending lead from the back of the gauge. Hook it up between the lead and ground and set the multimeter to the appropriate ohm range. Once you've got a steady reading in the right range move the float up and down and see if the resistance changes. That'll answer that question.
If the sender is operating properly make sure the gauge is getting power and if it is then replace your gauge.
A generic diagram of the system I found on the interwebz: