how to remove stains from outside of pots and pans?

Depends on the type of pan. On non-finished aluminum you can use just about anything, easy-off with a scouring pad. On stainless steel, a light coating of cooking oil and steel wool gets most stuff off. If it's a nice pan however...like copper or polished steel, be very careful and use a non-abrasive chemical method, like soaking some paper towels with a non-reactive cleanser and letting it sit on the pan for a few hours/overnight.

If they're copper-bottomed, a good brass/copper cleaner would work. Brasso is really good for this. If they're stainless steel, there is a stainless steel cleaner (spray can) on the market that also works well. I've got a frying pan that I absolutely LOVE...non-stick interior, but it's neither on the bottom (aluminum I think), so I'm resigned to it looking horrible because the inside is still perfect! LOL

As for any that are neither...try steel wool and a strong degreaser. Most buildup on the bottoms are from oil and grease and the more you use it, the harder the residue gets and the more difficult it is to remove!

Good luck!

Baking soda.

Mr. Clean Magic Eraser. I don't know what the hell is in these little sponges, but they are AMAZING! :)

use scrubbing bubbles and a scrubbing brush.