Try a Heavy Duty Mr. Clean Magic Eraser. Also try nail polish remover---but test in an inconspicuous place to make sure you don't strip the color.
What are the stains?
For tough stains, wet a melamine-foam sponge (Mr.Clean Magic Eraser) with water and squeeze out as much water as possible. Rub the stained area gently until the stain disappears. ALWAYS TEST THE SPONGE ON AN INCONSPICUOUS AREA FIRST to be sure that it doesn't damage the surface
If it the yellow stains that occur under rugs or furniture, that a chemical reaction that has actually damaged the vinyl and all you can do is leave it uncovered and hope it fades.