What to do to help my dirty tile floors?

You can always put runners over the high traffic areas. But, if you want to really fix the problem i would steam clean them again, and/or use a tile cleaner from a hardware store or tile store. Be sure you purchase the right tile cleaner for your tile. The employees should be apply to help. After you throughly cleaned the tiles, try re-sealing them and the grout. If you seal your tiles and grout it should protect them from getting dirt dug into them. But, before you reseal them you need to make sure they are truly 100% clean otherwise all the other dirt and grim will be stuck inside the seal. If possible, you may want to hire a professional tile cleaning company to clean them before sealing.