Heat up 1 cup of white vinegar, mix in about 1/4 cup of Dawn Premium. Not the dollar store kind, because it is too thin. When mixed, pour into a spray bottle and fill with water. Shake. Spray down the grout and let it sit overnight. In the morning rinse. If you have stubborn stains, spray again. Use this mixture a few times a week. It will keep your grout and tiles clean. Also works wonders in the toilet bowl to keep hard water stains at bay. Oh you only have to heat the vinegar one time when you add the Dawn.
I use vinegar and warm water with a toothbrush and scrub. It's labor intensive, but it works.
Create a paste with baking soda and peroxide. Then brush the paste into the grout and let it site for about 15 minutes. Then clean it up and if your grout is white it will be white and clean.
Lysol Lime & Rust Remover Toilet Bowl cleaner, comes in a black squirt bottle. Scrub with Scrub Daddy or Mr. Clean Magic Eraser. Make sure to seal once you get it clean. If you don't get it clean, you can paint with grout paint or exterior paint (what I used in 2005 - still looks good) and seal once the paint is dry.