Dirt and scuff marks don't adhere well to vinyl, so you can get most of them off with a solution of 1 to 2 ounces dish soap per gallon of warm water. Use a non-scratch kitchen scrubber to loosen stubborn marks. If you need more cleaning power, use a solution of 1 part white vinegar to 1 part water. Avoid strong solvents such as mineral spirits as they can etch vinyl, which results in a dull finish.
Cleaning Yellowed Vinyl
Vinyl usually turns yellow because it's exposed to prolonged and frequent sunlight or because it's defective. A chemical reaction causes the yellowing so you may not be able to remove it. You may have some success with a solution of 1 part bleach to 2 parts water. If that doesn't work, try undiluted white vinegar. Allow the vinegar to remain on the vinyl until it dries, then wash it off with clean water.