Tile and grout cleaning without the proper equipment can be very difficult. In my experience people would rather attempt it themselves or even hire a house cleaner to perform the work. Unfortunately, if it has been years since the last true cleaning of the tile and grout the results will most likely be unsatisfactory; I have witness this more than once.
If neglected the acidity of the soil and grease will literally eat the grout. The problem is soil and grease are very tough and require a combination of procedures to be removed. A strong chemical and a course brush will only go so far. For the best results nothing beats hiring a professional steam cleaner. Steam cleaners can clean tile and grout at 1000 psi. That means pressure washing the surface and the grout. That in combination with brushing, heat and industry strength chemical (usually an alkaline) results in a much deeper,faster and thorough cleaning.
At this point sealing grout with a high grade sealer will have the greatest effect. Grout and tile sealer is the first and last line of defense. A good sealer and proper maintenance will give tile and grout longevity and will preserve appearance. Sealer helps prevents moisture, stains, and soil from seeping into the grout and destroying it. It also makes for easier cleaning by hand. Sealer should be applied ever 1-2 years in high traffic areas or areas exposed to constant moisture i.e. bathrooms and kitchens. Other tile areas such as floors should be resealed every 2-3 years.