How do you clean terracotta tiles?

You could use a caustic soda liquid taking care to wear rubber gloves if necessary - just in case - and not to splash around; In fact when I did it I used a mop and bucket! Afterwards rinse with clear water about 7 or 8 times or until the water begins to get clearer. I got great results with lots of dirt and muck removed! Then I gave them the linseed oil treatment. The method I used involved diluting linseed oil with white spirit (a 50/50 mix) and applying to the tiles in numerous coats. You may find it takes quite a few coats depending on how porous your terracotta tiles are, but you should end up with a shiny finish - that way you'll know they're properly sealed . For future cleaning do exactly the same.