Measure and pour the white vinegar and the table salt into one of the glass bowls. Stir the ingredients to dissolve the salt.
Place the pennies into the bowl and stir them around gently with your fingers.
Soak the pennies for about five minutes.
Dip an old toothbrush into the vinegar solution, and scrub the surface of the pennies with the bristles.
Remove the pennies from the vinegar and salt, and place them onto a layer of paper towels.
Pour the baking soda into the other small bowl, and add enough water to make a gooey paste.
Place a small dab of baking soda paste onto a penny and work the paste into the surfaces of the penny with your fingertips to polish the penny. Continue polishing the penny until it shines.
Rinse the penny under cool water, and buff it dry with a paper towel.
Repeat the same polishing process with each penny.