Run cold water over the grape juice stain for two to three minutes to flush it.
Pour lemon juice over the grape juice stain. Scrub on the stain with an old toothbrush. Allow the tablecloth to air dry.
Combine 1 tbsp. white distilled vinegar with 1/2 tsp. liquid laundry detergent if the grape juice stain remains. Pour the mixture into one quart of warm water. Soak the stain for 15 minutes and then rinse the tablecloth with clean water.
Launder the white tablecloth with your preferred detergent and the hottest water setting possible. Add 1/2 cup chlorine bleach to the dispenser to help whiten the tablecloth.
Remove the tablecloth from the washing machine. Hang the tablecloth to dry.
Blot the stain with rubbing alcohol or undiluted white vinegar if it remains. Launder the tablecloth with chlorine bleach again and hang it to dry. Repeat the stain removal process until you remove the grape juice from the tablecloth.