How do I clean the stains in my stainless steel kitchen sink?

Brillo

Soft Scrub with a slightly abrasive sponge

Stainless Steel cleaner (white cream)

Buy Bar Keeper’s Friend.

^^^ Agreed. The stuff is nonabrasive, so it wan’t damage your sink, yet highly effective at removing grime and stains.

@SnipSnip I found some stainless steel Bar Keeper’s Friend on Amazon for $6. I will order when I have the money. Thanks I will update Fluther when I use it.

@all My friend suggested Dawn platinum that cleaned her stainless steel sink fine. I will try that first. Then the Bar Keeper’s Friend. I will be able to buy soon in town, and not have to wait weeks for Amazon to deliver.

DO NOT use steel wool!!! The steel fibers will get into nooks and crannies of the sink and will cause rusty pits.
Use an abrasive cleanser like Comet.
(These suggestions came with my stainless steel sink.)
They mix the element chromium into the steel so that it will resist rust.

Ordered
Dawn Platinum Powerwash Dish Spray, Dish Soap, Citrus Scent 473 mL for ~$4.50 free delivery. Will arrive Wednesday.

Stainless steel is more resistant to rust (stains) than plain steel. Treat it nicely (as professional chefs would) and it will look good for a long time.

Update the Dawn Platinum worked. My sink is clean.