Place the plastic cups with hard water stains in a dishpan. Pour full-strength white vinegar over the cups until the stained areas are covered. Allow the plastic cups to soak for at least one hour or overnight, if possible.
Scrub the hard water stains with a nylon mesh scrubber or sponge to remove the loosened mineral deposits. Rinse the cups with water.
Create a paste in a bowl to remove the remaining hard water stains. Pour 2 teaspoons each of lemon juice and baking soda into the bowl. Stir the two ingredients to create a thin paste.
Dip the nylon mesh scrubber into the lemon juice and baking soda paste. Apply it to the remaining hard water stains and allow it to sit for 10 minutes.
Scrub the plastic cups to remove the hard water stains. Apply more paste as needed until the stains are completely removed. Rinse the cups with water.
Fill the dishpan with warm water. Add three to five drops of dishwashing detergent. Wash your cups to remove any remaining lemon juice and baking soda paste residue.
Rinse the cups with water and dry them with a clean kitchen towel.