To get hard water spots out of stainless steel sink, you first need to run some very hot water into the sink. Fill the water to the rim, and then pour a cup of household bleach into the hot water. After this, pull the plug and rinse your sink well. Get some cleanser and use to scrub your sink with. After you have scrubbed it thoroughly, rinse all the cleanser from the sink. SOS pads are good o be used for scrubbing.
You can use Bar Keepers Friend with a white (not green) non scratch 3M pad. Always make sure you scrub WITH the grain of the stainless steel so you do not add visible scratches! Never use steel wool to scrub as you will leave leftover steel particles that will be difficult to remove and will rust when they get wet.