A moss problem (usually found in older lawns) is usually indicative of an area where the soil is compacted and there is poor drainage. Typically, the areas are also in the shade.
To correct the problem, the environment needs to be altered. The drainage needs to be improved and sunlight needs to be filtered through or introduced under the canopy. The moss can be chemically or physically removed from the site and the grass re-seeded in the area should be well-suited to survive in the shade. The grass should be fertilized in the shady areas so that it will be dense and healthy and able to withstand any future potential moss invasion.