Mist them with vinegar and let sit. Then scrub with a mildly abrasive pad, like the yellow and green 3M cleaning sponges. You may need to repeat the vinegar treatment, but it will eventually dissolve the mineral build up.
Prepare a mix of half warm water, half vinegar and a small drip of dish soap. Apply to window with a sponge and then wipe with crumpled up newspapers! Repeat if you don't get it all off the first time. You will have bright shiny windows that stay clean for quite some time!
Vinegar to dissolve the deposits. Then clean with damp microfiber cloth. You will need to use distilled water with the microfiber cloth to prevent it from happening again.
I use the water, vinegar and dish soap method also. For the shower door I add a good squirt of dishwasher rinse aid like Finish. I also let it sit for about 20 minutes and then use a 3M mildly abrasive pad to scrub. Rinse and wipe dry with microfiber cloth.