Fill up a small bowl with warm water. Add in baking soda and mix together. Stir with a spoon until a sticky paste is made. Add more baking soda if necessary until it has reached a pasty texture.
Stir up the pasty substance until it is sticky to the touch. Apply the paste to the vinegar spot by hand. Cover up all of the spots of vinegar with as much of the baking soda paste as needed. Do not leave any gaps or cracks in the baking soda.
Wait for the baking soda to dry up and harden. Dry time will vary depending on the size of the vinegar spot and the amount of baking soda necessary to cover the area.
Wipe up the paste once it has hardened with a wet, soft towel. Run the towel over the entire area and empty the baking soda paste into the trash can. Pat down the area with a dry towel. Dab at the vinegar spot, but do not wipe it at all.
Inspect the area and make sure the spot has been completely removed. Repeat the process if the spot still remains on the marble.