Mop the basement floors and walls with hot, fresh water. If the salt deposits have not yet reacted to the carbon dioxide in the air, the hot water will be enough to remove the stains.
Pour a quart of white vinegar into a gallon of hot water and mop the floors again if deposits remain. Or dip a scrub brush into the solution and scrub at stubborn salt stains on the concrete walls of the basement. The vinegar's acidity helps break up the salt if it has already started to react with the carbon dioxide in the air. Once this reaction takes place, the salt becomes more difficult to remove.
Apply a stronger acid-based concrete cleaner to the basement surfaces if salt deposits remain. Wear rubber gloves and safety gear since these cleaners are highly corrosive. Follow all instructions on the packaging for best results.
Sprinkle baking soda over the areas where you applied the acid-based cleaner. This helps neutralize the acidity and makes the cleaner safer and less corrosive after it's had a chance to work.
Rinse the basement concrete with fresh water and dry thoroughly with a towel. The salt deposits should be gone.