I wash with a mixture of hot water, vinegar, and a little dish soap. Scrub with a rag (and brush where needed) dry with an old towel. My tile is supposedly textured, but it still gets very slick when wet. In between scrubbings I use a steam mop, but that does nothing for the grout.
I loathe and despise my tile floors. I will never put it in myself.
Next time I want hardwood, cork, or maybe stone tile in the kitchen.