What do I use to clean a tile floor?

My mother-in-law's house was built in the 1950's. Her parents lived here before she did and the tile in the kitchen needs a lot of work. There's grim and grit stuck on the floor around the stove, sink and fridge. The tile in the other areas is dingy and kind of gross. No regular floor cleaner has been able to really clean it. And, as far as I can tell, there's concrete under the tile and the lines in between the tiles are very thin. My dad did installed tile and I remember that he used an acid wash to clean the tile after it was grouted. So I was wondering if I could use an acid wash to get the tile clean? Could I use bleach and water? What can I use to get that grim up and thoroughly clean the tile?