The best way to mop a floor varies, depending on what kind of floor you have. For example, wood floors benefit from a very light damp mopping with cold water and a mild wood-friendly soap solution, while stone floors can be washed with hot water and more aggressive soaps. While the basic mopping technique remains more or less the same in all cases, your choice of soap is crucial.
Before you mop a floor, gather the supplies that you will need, including a mop, a bucket, a cleaning solution of choice, and a broom. Rag mops are best for textured floors, as they will actually lift dirt from the floor, while sponge mops are great for smooth floors. As a general rule, use mild cleaners on stone and tile, while more harsh cleaners can be used on linoleum. On wood and Pergo flooring, you may want to avoid using soap, unless the installer of the floor has specifically recommended a particular type of soap, as you do not want to damage the floor.
Start by clearing the floor of all objects and debris. If you are going to be cleaning in that room, do it before you mop the floor, so that you do not knock dust and other materials onto a freshly cleaned floor. Take the time to shift furniture to another location while you mop a floor, to ensure that you really clean the whole floor. Then, sweep or vacuum the floor to pick up large chunks of debris.
Fill your bucket with hot water and your soap of choice; if you want an especially sparkling floor, you can use vinegar, but be aware that vinegar may stain or damage floors made from wood and stone. Dip the mop into the water, wring it out well, and start mopping. Rag mops should be moved in a figure eight motion, while sponge mops can be swept across the floor in a straight line. Work from top to bottom of the room towards the door while you mop a floor so that you don't end up mopped into a corner, and dip and wring the mop frequently to flush dirt from the mop.
If you have not mopped in a long time or the room is especially large, you may need to change the mop water partway through your mopping session. It pays to take the time to do this, as otherwise you will be smearing dirt across the floor, rather than fresh water and soap. After you mop a floor, allow the floor to dry completely before moving items back onto the floor, and rinse your mop well, hanging it to dry so that it will not mold or mildew before you use it again.