how to get rid of hardwater stains from bathroom fittings

Hi everybody,
We recently moved to a rented apartment. Event though the apartment is well maintained, the bathroom looks dirty. That is only because of the stained taps, showers, closet etc. It won't shine even after cleaning with different cleaners several times. Can you please suggest me some method to or cleaners to use. Also how do we filter the water. What sort of filters are available?

Thanks