Tile and grout cleaning:

Every time you clean your tiles, the grout becomes dirtier. You see it in every commercial job (for example, in new restaurants). Several weeks after opening a building to the public, one can notice that the grout colour has changed considerably. It happens much earlier than in a domestic situation, not just because of the amount of foot traffic. Restaurant floors are washed at least once a day. This only speeds up the process of grout saturation with dirt. Normal cleaning can be described as pushing dirt from tiles into grout lines. Unprotected grout absorbs wastewater along with all its dissolved dirt and chemicals. There is no way around it except to seal the grout.
Some tools are better than others. You should use microfibre mops for standard clean-ups. Those carry just enough moisture to clean. Moreover, a good microfibre cloth catches dirt on contact. It pays to have several mop clothes to change them as you go instead of rinsing the same cloth in a bucket of water. The excess of water isn’t a good thing. The more water you use, the more wastewater stays in the grout. It always leads to grout discolouration. In extreme cases, deep stains might start showing through a glazed surface of a tile. Rinsing is as essential as washing. Remember that chemical cleaning products leave residue. The easiest way to rinse the washed surface is to add some vinegar to the water. Let’s say 1/3 a teacup of weak vinegar to half a bucket of water. This should get rid of alkaline residue without tipping the pH-balance the other way.

Cleaning silicone:

Mold loves silicone. Mold spores invade it much more quickly than grout. In order to keep silicone clean, you should use BLEACH. Remember that bleach can damage your coloured grout. Use good old fashioned Janola with a cloth rather than something in a spray bottle. Wet the silicone lines using a sponge or a cloth. Let the bleach sit for a minute or two to kill mould spores. Rinse bleached areas with clean water. Do not leave bleach residue. It is still important to be careful even when the grout is white, as there are multiple shades of white. It is indeed possible to make white stains on white surfaces if you really try.

And here is how non-professionals do it the perfectly right way (providing we’re dealing with WHITE surfaces). If you have coloured grout do not leave the bleach on fro longer than a few minutes. You could play with masking tape and foil, to cover anything that’s not silicone. That would be a bit too risky for my taste.

Routine cleaning of stone (marble, granite, basalt, sandstone, terracotta, slate)

Indoors and outdoors, it’s a different story. While working outside, you will have a chance to hose off tiles with plenty of clean water. Hence, you can use a full bucket of detergents and a scrub brush. Although dirty water will soak into grout, you will have a chance to rinse it properly. Be careful with sandstone not to scratch the surface. Your scrubbing brush shouldn’t be too stiff (and never a metal one). Use hot water if you have a chance. Always rinse the tiles with heaps of fresh water after cleaning.
While working indoors, your cleaning efforts should be limited to the use of microfibre mop as described in “Routine cleaning of tiles“. It helps to have a wet/vac. If you’ve got one, you can allow yourself to use a decent amount of water to rinse. I’m not talking about leaving heaps of water on tens of square meters of tiles and hoping to vacuum the lot before you flood a building. You have to split a job into small, manageable areas that you could rinse and vacuum without flooding a house. That is about all you should be doing with your tiles. Anything beyond that is a profession.