Leave the mattress outdoors in full sunlight to dry.
Clean off any surface damage, such as dirt or grime, using rags to brush off both sides of the mattress. Do not grind the dirt into the mattress, but use a light touch to brush away the dirt.
Mix equal parts rubbing alcohol and water in a bucket. Dip a clean cloth into the solution. Wipe down the entire surface of the mattress, dipping the cloth in the solution as necessary.
Place the mattress in a sunlit room with open windows. Place fans around the mattress to speed up the drying time. Flip the mattress when the top feels dry to the touch.