How can you get an old white kitchen sink to be white & smooth again?

What is it made out of?

Comet cleanser

Here's some info it it's porcelain.

https://www.wikihow.com/Clean-and-Shine-a-Porcelain-Sink

If it has yellowed badly the top layer of porcelain has been worn off. You can temporarily bleach it with a cleanser containing bleach or you can resurface it. There are companies that come in and do it or you can purchase a kit and try it yourself. Ask at the paint counter of any big store like Home Depot or Lowe's.

Use some of the cheap toilet bowl cleaner liquid and will make it white again as long it is made of porcelain.

magic erasers help to clean it with whatever cleaning product you are using.

Bar Keepers Friend works well on porcelain. I have a white solid surface sink and the only thing that cleans it anymore is Oxiclean or bleach.