Wash the tabletop surface thoroughly with Murphy oil soap and water. Allow the tabletop to dry.
Dampen a cloth rag with denatured alcohol. Gently rub any white water rings on the surface of the table with the cloth rag to remove them.
Rub the areas where you removed the water rings with steel wool. Buff the area with paste wax using a clean cloth rag until the sheen is restored.
Touch up any small scratches in the tabletop with a touch-up stain marker. Allow the touch-up stain to dry.
Apply paste wax to the touched-up area and buff it to a sheen with a cloth rag.
Fill in any shallow dings in the tabletop with a tinted wax stick. Apply paste wax to the filled area and buff it with a clean rag.