You scrub your tile floor until you are certain it is clean, and then it dries, and you discover spots. Lots of things cause spots, but one of the biggest culprits is water. If you use tap water when cleaning your tile floors, then it is likely that you will eventually have spots. If you use well water that isn't conditioned thoroughly, you can end up with rusty spots, too. Most tap water is full of dissolved minerals that can interact with certain types of tiles and leave white spots. The other product likely to cause spots is soap.
Vacuum your tile floor thoroughly using a non-beater bar vacuum cleaner. Beater bars can drag grit and scratch tile.
Mop your floor using a pH-neutral floor cleanser, hot water and a mop. Dry immediately with towels.
Steam the floor with a commercial steamer and use a product recommended for your type of tile to remove or strip wax. The steamer adds heat. The wax stripping product will have exact directions on how to use it on your floor.
Mop your floor again and remove all of the residues by frequent rinses and changing the water and cleanser. Dry the floor immediately with towels.
Scrub the grout with a nylon bristle brush and an old toothbrush and a recommended grout cleanser. The steamer should have lifted any stains that were in the grout, but if you have persistent stains, go back and forth between the grout cleanser and the steamer until you are satisfied.
Wash the floor again. At this point you should see noticeable changes in any stains. Many spot type stains become trapped under layers of wax and they remain after the floor is washed. By stripping any wax or polish off the floor to reach the tile surface, you should remove yellowing, white spots and other stains.
Rinse the floor using distilled water. This is a very important step since distilled water will not leave mineral deposits. Immediately dry the floor with a dry towel. Most spots are caused by using non-pH-neutral soap and mineral-rich water that is left to stand on the tiles. Always dry your floor by hand.
Seal your grout with a grout sealer and a disposable brush. This will protect grout from staining. Most floor tiles that have a shiny or glazed surface should not be sealed, so just seal the grout and wipe any extra sealer off your tiles.
Preventing spotting is as easy as the right soap, distilled water and drying your tiles with a towel. Frequent vacuuming will keep grit from scratching the tiles, and always clean up stains immediately.