You have to clean the entire floor normally and pick up any loose dirt and dust. If the grout has an old, worn grout sealer layer that still allows the water to collect, use a floor finish stripper to remove the sealant from the surface and rinse the floor with clean water and let it dry.
Now you have to apply a commercial grade grout cleaner according to the directions given by the manufacturer of grout cleaner and start scrubbing with a nylon bristle brush or an old toothbrush. You should work in small areas and rinse the cleaner thoroughly with water before you proceed to another section.
It is important to know that you need to remove mold before you start working on the stains left by the mold. You should put on your gloves and eye protection gear and apply a mixture of ¾ cup of bleach in a gallon of water over the patches of mold and let the mixture work for half an hour before rinsing with clean water.
To check the results, you can compare the sections that you have cleaned with the grout in low-traffic or protected areas. The stains often come from different sources, so all of the stains do not react in the same manner to a grout cleaner. In case you have tried one method that did not work well, you must be ready to try another one such as scrubbing with a concentrated white vinegar. You have to let the vinegar solution penetrate into the grout for about 15 minutes and then rinse with plenty of cold water to neutralize the acid from the vinegar.
It is good to know that the cleaning grout can be a frustrating experience when it is not completely clean after the first attempt, but you must resist the temptation to use super powerful cleaners. Muriatic acid, for example, can remove stains but it will damage the grout as well. Therefore, it is advised that you read reviews before you think of any such material to use.
When you are fully satisfied with the cleaning result, rinse the floor once more with clean water to remove or neutralize any residue of the cleaner you used.
We all like to finish soon, but if you rush to finish the cleaning phase during this project and start to seal the grout prematurely, you can turn a solution into a permanent problem because, in addition to sealing the grout, you will also seal the spots.