First choose the product you want to use to mop your floor. For most floor surfaces a good choice of cleaning solution is simply a mild dish washing detergent diluted with water. So fill your bucket or sink with it and with hot water.
 Make sure that you do a thorough sweep job before beginning to mop. Mopping up things that could have been swept is a waste of time and energy. So, sweep first, and do a good job.
 Next you want to make sure that as you clean your floor you change your water very regularly. If you let your water get too dirty, then essentially you are making your floor more dirty, not clean. This is sort of pointless. So, change your water when it starts to look dirty.
 After you have gone over the whole floor, you will want to then rinse the floor completely. You want to do this after cleaning because the soap you used to clean attracts dirt, so if you do not rinse the floor off you are going to have a really dirty floor again really quickly.
 Wash your mop in detergent solution, after use. If you do not clean your mop after use then you will be washing your floor with something that is not clean. How can your floor get clean if the thing used to clean it is dirty? You can't. So, wash your mop out well. How you wash it depends on what kind of mop it is.
 Keep your mop as dry as you can. When you mop your floor, you want to squeeze out as much of the water from your mop as possible. The drier it is, the less dirt you spread, and the better job picking up dirt. You will want it to be damp, of course, but not sopping.

One of the things that makes the biggest difference when it comes to mopping your floors is the type of mop you use. There are tons of mops on the market, and they all claim to be the best. However, for most floors, you can use a light cotton mop. These are generally light weight, and thus easy for you to handle. They generally are easy to clean, so you can keep it clean and washed after use so you do not have to replace it often. Also, if you use one, and push it don't drag it, it will likely pick up more than any other kind of mop. Just be sure you keep the floor as dry as you can, and you wring the mop out properly.

Now you know how to mop, so enjoy having clean floors by employing good mopping habits regularly.
One last things, is that do not let yourself be talked into a flat sponge mop, or mops made of any other material other than cotton. Not only can these be expensive, but when wet they are very heavy to use which could hurt your back. And, they simply do not produce as good effect as a cotton mop. Also, do not buy a super expensive cotton mop, a cheap cotton mop is as an expensive one.