Having a few techniques for cleaning grout in your homemaker's toolbox would be a good thing for almost everyone, as most if us have (or will have) tile floors or walls somewhere in our homes.
I don't know why we are so insistent on tile. I have it, but I also have a love-hate relationship with it.
How to Clean Ceramic Tile
Don't use a sponge mop or squeegee for tile floor cleaning. It will end up leaving residue in the grout. Use an absorbent microfiber or chamois type mop instead with one of the solutions below.
1. Tile is not porous. For general maintenance, very warm water may be enough unless the floor is greasy. If the floor is greasy and the grout is sealed, add 1/4 cup of white vinegar to 1/2 bucket of hot water. Never use an acidic cleaner (i.e. vinegar and water) on a tile floor if the grout is unsealed.
2. Place 1/2 c of borax in a bucket. Gradually add 2 gallons of hot water so that the borax doesn't splash. Wear gloves if you are going to touch this solution, as borax can be irritating to the skin.
3. If the grout is not sealed, from time to time give it a good clean using the directions found below.
Preventing Grout Stains
Remember the old saying - an ounce of prevention is worth a pound of cure? grout is one of those areas where a couple of hours invested in sealing can prevent hours of work cleaning grout later. There are a number of sealing products - most of them come in little bottles with a sponge just the size of the average grout line.
The sealing products I have looked at at the hardware/DIY store have been fairly toxic when wet, so please pay careful attention to the safety instructions. Don't touch or inhale, and don't allow pets or small children in the room while the sealant is drying.
I have to be honest though - although lots of people talk about using a sealant, few of us actually ever get around to it.
Don't go barefoot on tile surfaces, and keep humidity under control. Body oils are one of the major causes of staining of grout on floors. It causes light colored grout to gradually darken over time. Wearing slippers and using bath mats can extend the life of your light grout, and reduce the amount of treatment time.
Keeping moisture under control helps to reduce the chances of mold or mildew, especially as your grout gets older and more porous.
Environmentally Friendly Methods for Cleaning Grout
Simple Baking Powder Paste Depending on how much grout you want to clean, mix a batch of baking powder and water in a bowl, adding just enough water to make a runny paste. Using a scrub brush, scrub it into the grout lines and allow to dry. As it dries it will absorb dirt and oils out of the grout. Vacuum the excess and rinse with clear hot water. (I use a microfiber cloth to rinse with - it picks up all of the baking soda residue)
Hydrogen Peroxide Depending on the stain, hydrogen peroxide straight out of the bottle can do a good job.
Baking Soda and Dish Soap Paste Used with a scrub brush, this can work wonders if the stains don't come out with baking soda and water alone. You may need to add a little bit of water for a workable consistency, but otherwise use it just like the the simple baking powder paste above.
The Method of Final Desperation
This for when you have tried ever grout cleaning method, and your grout still looks totally gross.
Get a grinder and a wheel specifically made for removing grout available at most hardware/DIY stores. Turn it on, remove all of the existing grout, and re-grout.