Here's a tip I found on Pinterest that actually did work. (See also, Pinterest Failures) The tile floor in our new house is really dirty. I didn't even realize how dirty until I got down on the floor to scrub the grout. I used this grout cleaner recipe I found via Pinterest and it actually worked! My grout did not get quite as clean as hers, but it looks WAY better. Probably I am lazy and didn't scrub hard enough. I also tried doing the entire process twice, but I didn't notice a difference the second time.
Anyway, this is my actual floor where I just cleaned one tile. This is after the whole area was mopped and dried - that dirty grout is not wet.
I discovered that the scrub brush I was using cleaned the tile itself really well, even with just water. You can see a difference on the tiles an inch or so around the grout. The tile I cleaned practically glows. So now I have to scrub all the tiles, too I've done about 1/3 of the area that needs to be cleaned. It's definitely a lengthy process, but the difference is amazing.
Here's the grout cleaner recipe I used:
1 3/4 c. warm water
2 T. baking soda
1 T. and 1 t. ammonia
1 T. vinegar
I got a small Scotch-Brite scrub brush at Target for $2.50 - it was called "hand and nail" brush. I bought a larger one for scrubbing the actual tile. I sprayed the grout cleaner on, and let it soak in for 30 minutes or so. It's definitely easier to clean the longer you let it soak. Then, I scrubbed the grout one line at a time. I wiped the dirty water off with a rag, and rinsed my brush in a bowl of water in between scrubbing each line.
I cleaned each area after scrubbing, so that any dirty water wouldn't soak back in. That's it! Maybe in a week or so I will actually get it all done.