Use dry mop on regular basis to clean the dirt on the laminate floor. Vacuum cleaner is also a good solution to remove dirt easily. You can also use hot water for cleaning without getting streaks. Then use dry cloth to make the floor dry, or let it dry naturally. There are other process also to clean the laminate floor easily - by using vinegar & water solution over the affected area to get the shine back.
Try using a product that specifically lists a streak free finish as one of the main product features. Often those streaks are left from residue or from your mop itself. Change your mop head regularly and go over the floor with plain clean water after to reduce the soap residue on the floor.