Moss is an opportunistic plant that spreads by spores. If the conditions are wrong it is impossible to grow, if they are right it is tough to eradicate. The lawn in one of the most difficult places to have moss. You can start discouraging moss by focusing on lawn health. Initially you can use an iron-based moss killer remove it. The moss will continue to return each year until favorable conditions are corrected. Expect it to take a few seasons to get ahead of the moss.
Lawn grasses love sun, moss does not. Too much shade will proliferate moss and cause sparse weakened turf. By using grass seed formulated for shade you will create yet another problem. There will be a distinct line where the sun and shade grasses meet. This will create the same two toned affect you are trying to avoid by removing the moss. It would be better to remove trees or cut enough limbs to allow the sun in. You can also remove the grass in the shade areas altogether. Replace the grass with shade plants, or evergreen groundcovers.
The right soil pH is critical for a healthy lawn. Turf grasses require a neutral to slightly alkaline soil. The optimum soil pH should be between (6.5 and 7.0). If it is lower than this it is acidic. Mosses thrive in acidic soil conditions. Find out what is typical for the native soil in your region. The pH is also important for proper nutrient uptake in lawn grasses. The easiest way to bring up the pH is by adding lime to your lawn. In areas where soils are naturally acidic this should be done every year. It is nearly impossible to overdo lime. This is one of the safest, easiest and least expensive steps you can take to combat moss. Do this in the spring or in the fall. It is completely acceptable to lime in both seasons until the pH is improved.
An unhealthy lawn allows aggressive plants like moss to take over. Make sure the lawn is getting fertilized properly. Organic fertilizers are best. They improve the soil structure while adding nutrients. Many commercial based organic fertilizers can be applied with a spreader. Chemical-based nutrients work fast then disappear, doing nothing for soil health. What is worse is that chemical fertilizers create an acidic environment. The nitrogen will green up the lawn but then leave acids and salts behind. A thin layer of organic compost sprinkled on the lawn as a top-dressing each year is another way to fertilize and improve soil. Fertilizing in the fall will give the lawn a head start for spring.
Moisture and Drainage
Moss grows where there is consistent moisture. Let the lawn dry out between each watering. If the soil is moist all of the time you will need to correct the problem. If soggy soil is being caused by bad drainage, fix it. You may need to install drainage pipes or a French drain. The water could be coming from an underground spring. In this situation it may be better to change the grass to moisture loving plants in that area.
The moss will turn black when it is dead. Carefully rake away the moss and dispose of it. If it is a thin layer it can be left in place to break down naturally. The spores will have already been released, so leaving the dead moss in place will not further the problem.