Use the dull edge of a plastic putty knife to scrape off and loosen stuck-on stains. These include things like old food, gum or dried lacquer.
Wet a cloth or scratch-resistant cleaning pad with warm water. Add a little non-abrasive, non-detergent soap to clean stubborn stains.
Wipe the counters down with the wet cloth. Use a vigorous scrubbing motion to remove stubborn stains.