Sweeping a laminate floor is a mistake.
I know it sounds strange, but a traditional broom is not your best bet with a laminate floor. You need a dry dust mop, or a vacuum cleaner to get the job done. Personally, I prefer a dry dust mop. Regular brooms will leave behind too many particles. Particles mix with the wet mop and get spread around on the floor. At best they'll leave streaks and residue behind. At worst, they'll scratch and pit the surface of your floor. Either way, a broom is not the way to go. If you do decide to use a vacuum cleaner, a machine that has an on/off brushroll button or a hard floors setting will be best. Brushrolls are capable of scratching and damaging laminate over time.
Laminate floor cleaner is not a necessity.
I know some people have a specific brand that they love and won't give up, but an expensive laminate floor cleaner is not always the answer. Choose a cleaner that is designed to work with your floor type and fits in your budget. Give homemade mopping solutions a try. Sometimes just a little water goes a long way. Whatever you do, don't use too much cleaner. Using too much soap is tempting when you really want something clean, but all it does is leave a residue behind that dulls the finish of the floor. Residue is the leading cause of dull looking laminate floors.
Liquid isn't good for laminate.
I know. How are you supposed to clean something without water. Water and other liquids can actually seep in between the laminate boards and cause swelling damaging the laminate. You don't need a ton of water or liquid to clean these floors. Be cautious about having too much. Try only spraying as much as you need on a section of floor as you mop. If a lot of water or liquid is left behind after you mop a spot, you're using too much. The floor should be able to dry on its own within 1-2 minutes of you mopping it.
Buff the floor to shine it.
If you really want to make sure that your floor shines, you'l need to take a few minutes to buff it dry. Try using an absorbent clean cloth or mop head. In my experience, cloth diapers and microfiber cleaning cloths make the best buffing rags. Gently buff the floor to a nice shine.
Protect the floor.
Now that you know how to make the floor look great, keep it looking great by protecting it. Make sure you have indoor and outdoor mats positioned at the entrances of your home. Consider a no shoe rule in the house. Wipe up spills and messes right when they occur. Use furniture protectors on the bottom of large pieces of furniture to protect from scratching and pitting. Watch out for overfilling plants that may leak onto the floor. Be sure that the window coverings in your home can prevent the sun from damaging and discoloring places over time. These are simple things to do with your laminate floor that will prevent it from aging or being damaged prematurely.