Spray the area first with your general purpose cleaner. Allow the solution to “dwell” for a few minutes. Spray again if necessary.
Using your baking soda paste, smear the paste across the bristles of a soft cleaning brush and completely cover the area with the paste. Use paste liberally.
Begin wiping the tiles and removing any remaining solution and dirt with a soft damp cloth. If you want a really nice shine, wipe the area down with a clean microfiber cloth.