Don't start mopping before you sweep or vacuum. You'll likely end up moving a lot of dirt and gunk around instead of cleaning your floors.
Move furniture out of the way to make mopping easier and to ensure you get every inch of a room clean.
Block off the area you'll be mopping. You don't want pets and kids tramping in with dirty feet.
Use warm water if you're mopping with a bucket and not a spray mop.
Make sure to use a cleaning solution that's safe for your floor type.
Start from the edge of a room, so you don't get trapped while mopping
Don't be tempted to use a soaking wet mop. Too much water doesn't equal better cleaning. Too much water can make things dirtier, believe it or not.
If using a bucket, change the water when it starts to look dirty. Don't reuse dirty water. It spreads germs around.
If you can, go with a rectangular bucket. It will give you more room to dunk your mop.
Flush that murky water down the toilet. It's the most sanitary option.
Allow air to circulate in your home, so your floors can dry quickly once you're done mopping.