How to bring back the shine to a stainless steel sink?

https://www.apartmenttherapy.com/how-to-make-your-stainless-ste-57954

use a stainless steel product, that's what they are made to do. Weimans is the best.

Hands down, use Barkeepers Friend and a non-scratch scrubby.

Car wax works wonders.

It works great to shine up pots and pans too. Even removes scorch/burn marks (you have to be persistent and work for awhile but it doesn't take hard scrubbing, just a lot of it, and keep the product wet but not dripping wet). I have also used it to shine up solid brass (not brass plated - do the magnet test before using on brass - magnet does not stick to solid brass), remove hard water build-up from faucets and around fixtures with an old toothbrush, and to remove grease from the glasstop of my electric stove. I've tried products made to use specifically on glasstop stoves, and they just have not worked for me. I clean that stove top every single day after I cook something with a speciality product, and the grease still builds up - I can see it when I wipe. It drives me nuts, makes me think my house isn't clean, LOL. Just be sure to either use a soft cloth like flannel or microfiber or a non-scratch scrubby. Barkeepers Friend itself won't scratch, but some cloths or scrubbies will.

After you clean the sink, apply some baby oil.

Mix baking soda and olive oil to scrub it with then rinse wiyh hot water.