How do I remove kitchen stains without damaging the countertops?

Dear Mr. Know-It-All,
Glasses, mugs and plates have left rings on my kitchen countertops, and I have had no luck in removing them. Can you please advise how to remove the rings without damaging the countertops?
– Going in Circles

Ah, we know that cleaning the kitchen stains can be painstaking but it becomes easy-peasy once you learn the ropes. Since your countertop is probably made from Formica, Corian or artificial marble (in which case I hope you haven’t tried to use sandpaper to rub the surface), you can simply brush the surface with toothpaste, or wash it with some white vinegar. In cleaning Corian countertops in particular, you can also use the yellow-bottled Cif cleaner with a soft sponge gently.