Try plain old white vinegar. Soak a cloth with it and set over the stain. Let sit for 2 or 3 hours wetting the cloth with more vinegar if it starts to dry.
Ditto, and then just lightly scrub it away with a brush. I encircle the faucet area of the sink with strips of paper towel soaked in vinegar. I remoisten the strips as necessary, and a couple of hours later remove the towel strips and scrub with an old toothbrush. The white mineral deposit comes right off.
Our calcium and lime deposits were way beyond anything vinegar could address. We found a product called Diamond Magic at a local hardware store. We had a thick calcium/lime layer on the shower doors. I wound up using the product with Grade 0000 steel wool on the glass. It took almost a month to get the doors clean. I keep a microfiber cloth near each sink and wipe off all water spots after use.
