Cleaning with a solution containing rubbing alcohol and white vinegar and buffing with a microfiber cloth is the best way to clean a laminate floor and make it shine. It is best to avoid sweeping the floor or using large amounts of water on it.
Sweeping a laminate floor is not very effective because it leaves behind particles that may scratch or pit the floor. Instead, a dry dust-mop should be used to prepare the floor for cleaning and shining.
While commercial laminate-floor cleaners exist, they tend to be expensive and are not necessary. Instead, a solution mixing equal parts of white vinegar, rubbing alcohol and water can be used. Very little cleaning solution should be used. Too much liquid can seep through the laminate and cause swelling. Applying the cleaning solution with a spray bottle helps to limit the amount of liquid. If it takes more than about 2 minutes for the solution to dry, too much liquid is probably being used.
After finishing the cleaning, the floor can be buffed to a high shine using a microfiber cloth. Clean cloth diapers also work well for buffing because they are soft enough to prevent any scratches to the laminate surface.