First step is to dry vacuum (or sweep well). Then use warm water and a clean mop - change this water frequently. Do this once a week. Every fourth week, use a little pH neutral cleaner (often labeled "everyday cleaner"). Use professional products by Stonetech, Aquamix, or Miracle Sealants. Better methods require professional equipment - get professionally cleaned occasionally.
A dollop of a cleanser like Pine-Sol in a bucket of warm water will help mop up a no-wax vinyl floor in a jiffy. It cleans the floor, leaves no sticky residue and fills your home with a wonderful fresh scent.
For a really deep clean, try using a Mr. Clean Magic Eraser. While this is time intensive, you will really get into the texture pockets. Then wash with a mild detergent and rinse well. Apply two coats of Armstrong's vinyl floor refinisher/restorer. This will add a nice, new looking sheen and make future damp mop cleanups much easier.
I have had success with many different types of floors by using the on-the-market steam mops. They don't require any types of cleaner and are filled with water. Once the water heats up, it releases steam and disintegrates the soil on the floor. You merely pull the mop back and clean up any residue.
First you need to clean any chunks off of the floor, by sweeping or vacuuming. Then I would use an all purpose cleaner such as lysol that you mix with water. If you are willing to spend more money, I would suggest getting a steam cleaner for you floor, such as the Shark.
you can clean a wax vinyl floor by using a map for the floor. wipe the floor with a dry map until it became shiny. try to use any dirty clothes that cant be use.