The level mechanism is an arm on a pivot attached to the top of the fuel tank and capable on moving to touch the bottom on the fuel tank. To the other end of the arm is attached a hollow plastic float. The plastic float is buoyant enough so that, even with the weight of the arm, it floats on the surface of the fuel. As the fuel level changes, the arm goes up and down. The arm is attached to a potentiometer which send a signal to the car describing the angle of the arm.
Certain cars take an absolutely instantaneous reading from this arm, for example, the Alfa Romeo 155. It was always fun to drive one of these around a round about and watch it's fuel light illuminate when turning right and exiting the roundabout, turning left and seeing the fuel gauge leap up to half a tank.
My Volkswagen Bora takes a while for the fuel gauge to register a level but I know that when it's pointing down hill, it gives an artificially high reading and it reads slightly low pointing up hill. Several times have I left for work thinking I have enough fuel (we live on a hill and I park pointing down) only to find I need to fuel it up once the car has been on level ground for a little while. Also, the fuel warning message almost always first appears when climbing a long, steady incline.
This image shows the fuel level sender from a Mk1 Golf. You can see the arm, the float and the white circular plastic piece at the top of the image screws into the top of the fuel tank and contains the potentiometer and plugs into the cars wiring loom.