How should I clean tile floors?

Mop if large area, scrub brush and simple green. You don't want a bleach product...it may discolor the grout. If the grout is wide. Ive been known to use a denture brush.

https://www.hunker.com/12481274/the-best-cleaning-solution-for-tile-floors

If you are having trouble with grout looking bad you may need to reseal or you can actually restain grout to a different color. And the tile can be cleaned with any hard surface cleaner for tile.

Make sure to change you water frequently!!! If it gets cloudy, time for a new bucket. I'm a huge Clorox Clean up Fan and use on all my tiles areas including floors/shower/tub walls. WARNING: Keep away from carpet areas, the bleach included will take out the color of nylon and some polyester carpets. No rinsing is required. Sometimes I have to spot clean areas, let them sit and scrub with toothbrush and then continue to mop. I'm in the floorcovering business in Florida and married to a Tile Mechanic, therefore we have this cleaning thing down to a science.

Some Carpet Cleaning Companies do have the attachments to do grout cleaning aslo.

Make sure to use a delicate/soft cleaning product. You don't want something too harsh and abrasive.

Here's an answer that might help - https://chascrazycreations.com/easy-eco-cleaning-hacks-on-a-budget-for-your-home/