When I have hard water stains on any glass around my house I take some baking soda and mix the baking soda with some vinegar to make a paste then I allow the baking soda and Vinegar paste to sit for about 3 minutes and then I scrub the glass lightly with a brush.
Then after scrubbing the glass with the brush I wash the paste off with plain water.
To prevent hard water stains from appearing on the glass again be sure to dry the glass with a towel after cleaning.