Choose a mop based on your floor type. If you have a floor with a lot of texture, you'll wan the more classic white string or rag mop. If you have a smooth floor, a sponge mop will work well.
Prep the Floor
In order to prevent your floor from becoming a sticky, muddy mess, sweep or vacuum the floor thoroughly before ever touching the mop to the floor. This is a good time to prewash sticky or gunky spots that you notice when sweeping or vacuuming.
Fill Bucket or Sink
Some people prefer to use a sink instead of a bucket. At the end, you can just scrub out the sink. If the water gets too dirty, it's easy to let the water drain out, wipe down the sink, and start with fresh water. Other people prefer a bucket because it can be carried along the path of the mop and many have built in wringers. Whichever you choose, make sure you use hot water and a mopping solution appropriate for your floor type. Check the directions to be sure. Do not think that extra mopping solution will get you a cleaner floor, it will just leave a residue on your floor.
Dip and Wring Out
Dip your mop in the bucket and wring it out with a wringer or by hand. Too much water dripping from the mop can damage a floor or leave the floor with an extended drying time.
Mop from the top of the room to the bottom, so that you are always standing on unmopped floor. This will prevent tracking. Mop in straight lines if you are using a sponge mop. For rag mops, mop in a figure eight shape to use the design of your mop most effectively. When you encounter tough or sticky spots, rub quickly and press down with your mop onto the floor to scrub at the spot.
Rinse and Wring
Rinse the mop frequently in another side of the sink, or a different bucket. Dip in the mop bucket, wring and begin mopping again. When the mopping water becomes cool or dirty, it needs to be changed. Otherwise you'll just be painting dirty water back onto your floor, and making your own work more difficult. For hard to reach corners and edges, wash with a paper towel or cleaning rag.
Put Away Supplies
When you've mopped every section, thoroughly rinse your mop and mop bucket and allow to dry completely. Let your floor dry completely before walking on it.
Special floor types may need modified cleaning care. Know what type of floor you have, and follow the manufacturers directions.
Choose cleansers that are safe for your floor type.