You might give us a clue as to what kind of car it is.

In a classic fuel gage there is a float in the tank connected to a
variable resistor, (the sending unit) as the fuel level moves the float
moves with it changing the resistance and the gage moves with it.  The
gage is basically an ohmmeter.

It sounds like you either have an electrical problem such as a short (or
open) in the wiring or the sending unit. If you can find the lead going
to the sending unit (should be on top of the tank and may be accessible
from the trunk) disconnect it (with the key on) and see if the gage
changes.  Then ground it and check the gage again, with the lead
grounded it should read full, disconnected it should read empty (or vice
versa).

If that is the case replace the sending unit.  If not then you have a
problem with the wiring or the gage itself.

Oh, and check the fuse first!

Good luck!

Jeff DeWitt