Well, it may seem impossible at times, but with the right solution, it's a breeze.
An easy, inexpensive and non-toxic homemade solution is to mix a ? of a cup of vinegar, with a 1/3rd cup of lemon juice, and ? cup of baking soda into about two quarts of water.
Apply the solution using an electric toothbrush as a grout scrubber. If you don't have one, you can always use a old regular toothbrush.
Another non-toxic grout and tile cleaner that does the trick is to mix a solution of warm water with any high quality oxygen bleach.
Let it sit for a good half hour or so and then scrub the area well. Then just rinse it with some clean water.
If you have marble, limestone or travertine tiles don't use any of these mixtures and don't use any mixture that's acidic.
A mild grout cleaner that can be used on all tile, grout, and natural stone is to mix a paste of three parts baking soda to one part water. Let it sit on the area for about 10 minutes before scrubbing and then wipe the floor clean with a damp cloth.
Now you know how to keep your grout clean with green solutions!