I have smooth surface quarry tiles, but the grout between them gets very dirty. I have tried all sorts, including a steam mop. I also bought a long handled stiff brush, but I think I get the best results using a regular soft bristle brush. The soft bristles are easier to push over the floor and because they’re soft, I think they get into the nooks and crannies better. I put it outside to dry when I’m done.
(Best of all is getting down on my hands and knees with a scrubbing brush, which I can still do and get up again, but I’ll be damned if I’m going to!)