Where is the difference compared to normal shooting? It depends in which mode you are. In all modes with automated / half-automated settings the metering through the lens will compensate. If in Manual it will your job to check the exposure meter and do adjustments.
A polarizer reduces around 1 to 1.5 stops of light entering your lens, so expect slower shutter speeds at the same ISO and aperture setting. Like octarine said, the camera will compensate on all modes other than manual.
Of course. To achieve a certain filter effect you have to rotate the front ring of the filter. If the lens front element also rotates it can counter this. Possible solution: focus first, then rotate the CPL to get the desired effect, take the picture.