I like using plain old vinegar and dawn dish soap mixed together. It cleans tile and grout very easily!
scrub, scrub, scrub - baking soda is a good abrasive that helps get it clean, and the dish soap helps get the grime off. make sure to seal the grout once it is clean!!!
I would try the methods other hometalkers have said. Vinegar and bicarbonate. Then if all fails open a window and add bleech.