Clean with baking soda and water
To clean your stainless steel sink, just mix a paste of baking soda and water. Scratches may also be removed with a very fine steel wool. Simply give the entire sink a gentle once over and it will obliterate and hairline scratches. Simply wash the residue away and continue with the rest of your cleaning.
Remove water spots with vinegar
To remove water spots, simply dip your sponge in white vinegar and they should rub right off. Rubbing alcohol also works to remove rust if your sink is suffering from a case of the "crusties."
Use cream of tartar for stubborn stains
If stubborn stains seem to be ailing you (thanks to the last tenant), use a mixture of 3 parts cream of tartar to 1 part hydrogen peroxide and buff it over a stain with a cloth. Let the mixture sit and allow to dry before wiping away with a wet cloth or sponge.
Polish with all-purpose flour
To add an extra kick to your sink, you can polish it with none other than All-Purpose Flour. Toss a few tablespoons of flour into the sink and rub it (some pressure is needed, but nothing that should cause a sweat to break out) around with a soft cloth. Another method is to use club soda. Simply put the stopper in the drain and pour in some of the bubbly beverage. Buff it around with a cloth, drying to prevent water spots when done.