don't happen on stainless. Most likely you have aluminum, which is great, it just requires different care.

To remove the rust spots, try steel wool. The finish will not be as shiny, but can be polished using superfine grit sandpaper (I don't know which number, ask at the hardware store.)

Then to keep em shiny and protect against rust, us "barkeeper's friend" stainless polish (available at restaurant supply stores.)
You need to use it every day to maintain the protection.

HTH