An easy way to rid a laminate floor of grime is to use a weak solution of vinegar and water. Not much vinegar is needed to clean any residue that will not come up with a broom or plain water. Simply add about a capful of vinegar to a small spray bottle and fill the rest of the bottle up with water and you are ready to do some cleaning. I know that isn't exactly a scientific formula but with vinegar and water exact measurements are not all that important. I've seen some recipes that call for 1/4 cup to a 32 oz. spray bottle, 1/4 cup to a gallon of water, and some people swear by equal parts vinegar, water, and alcohol. Do a little experimenting to find what works to your standards.
Before you get crazy spraying your floor with the mixture you should understand that laminate flooring does not like to be wet. That is the main reason that the spray bottle is used instead of a regular mop. Use as little of the vinegar and water mixture as possible on the laminate flooring and rub the floor and dry immediately.
You have a few choices when it comes to getting the water droplets off the floor. You can use a rag or a highly absorbent dry mop. The mop is a good choice if crawling around the room with a rag isn't an option. If you have bad knees or have a hard time getting up and down the mop is the clear winner. I can go either way. Some days I don't feel like scooting around on the floor and other days I find it somewhat entertaining.
It is important to keep your laminate flooring from becoming dirty. Frequent sweeping or vacuuming will help to cut down on the need to use any liquid laminate floor cleaner. Clean up spills immediately and there will not be any stuck on junk that needs to be removed.