Keeping your floors clean can be problematic simply because there's so much area involved. If you have tile floors, regular sweeping is a good start, but tiles and grout both pick up stains, and eventually, you need a liquid cleaner. You can make a green cleaning solution with white vinegar, which contains acetic acid. As far as acids go, vinegar is relatively mild, but it's strong enough to dissolve stains and discoloration, and it's safe. Vinegar dissolves most stains in grout as well as on ceramic, but you may need to scrub a bit to remove stubborn ones.
Sweep the floor with a broom, and remove all the debris with a dust pan. Vacuum along the baseboards, and then run the vacuum cleaner over the floor to remove any lingering debris.
Mix a solution containing equal parts white vinegar and hot water in a bucket. Use the solution to mop the floor, moving the mop first in one direction and then in the perpendicular direction. Work the solution into the grout with the mop to remove the stains. Dump out the solution when it gets too dirty to use, and mix a fresh batch.
Wring out the mop when you've finished the entire floor, and then replace the vinegar solution with clean hot water. Mop the floor again with the water to rinse off the vinegar.
Clean stubborn stains out of grout by putting some of the vinegar solution in a spray bottle, spraying the grout directly and scrubbing with a stiff brush. A new toothbrush works well, but an old one may be too flaccid for the job. Do not use a brush that has metal bristles or coarse steel wool. You might scratch the tiles or wear away the grout.