How can I get my bath tub super white again? And my sink super shiny?

Clean it! and often

I clean it twice a day

Mr.Clean, Mr. Clean, Mr. Clean!

@dpworkin oh so good to see you Mr Clean get to work loll

ok a potentially more useful answer than saying Clean it! is that some use bleach and it works for them or others say those magic vanish sticks work

Soft scrub works wonders

Baking soda. Also, like many mentioned, clean it often. If there is calcium, rust or lime stains to start with, CLR it first.

SUPER WHITE? Have it re-porcelained. White, Bleach soak, peroxide wet-dwon, and Scrubbing Bubbles

If the sink is stainless steel,
http://www.barkeepersfriend.com/

@jaytkay I use that too. Good stuff.

Nothing will ever be super shiny again if you scour off the gloss surfac with an abrasive.

If this is plastic, no amount of scouring or bleach will restore it. Plastic stains permanently. If it really bothers you that much, perhaps you can put in a new one.

This is so easy even I can do it! Use Lysol Power Toilet Bowl Cleaner with Bleach.
No scrubbing. Just let it sit there for a few hours and then rinse.

I suggest the same cleaning paste that is used on boats.

Use an Eco Sense product.