Fill a clean sink with warm water and add hydrogen peroxide and baking soda. Stir until all of the baking soda dissolves.
Soak the white tablecloth in the sink for 1 hour. According to Susan Waggoner, author of "Classic Household Hints," the combination of the hydrogen peroxide and baking soda will lift any existing stains.
Remove the tablecloth from the mixture. Move the tablecloth to an empty sink.
Examine the tablecloth for any remaining stains. Pour 1 tablespoon of laundry detergent onto each remaining stain and let it sit for 30 minutes.
Put the tablecloth into a washing machine with other white fabrics. Add commercial bleach per manufacturer’s instructions and launder as usual.
Repeat this process whenever the tablecloth is slightly dirty to keep it crisp and white.