Moss in your lawn is more than a annoying weed, it's a symptom of conditions more suited to the growth of the moss than the growth of grass. Mosses like acidic, constantly moist, shady conditions while grass prefers neutral to slightly acid soil that dries at the surface and full sun. While you can remove the moss, if you don't change the underlying cause of the infestation, it will always return.
The first step in moss control is removing the existing population. The chemicals sold as moss killers usually contain ferrous sulphate or ferrous ammonium sulphate, neither one particularly harmful to humans or the environment. They turn the moss black and eventually kill it. Apply according to the directions on the package in spring or early autumn.
Use a garden rake or a thatching machine to remove the dead moss from between the grass stems. If you have only a small lawn, you may not need to apply moss killer, just use your rake with a little extra energy. Don't worry about damaging the grass. Some plants may come up with the moss, but since grass plants spread from the roots, small bare patches can fill in quickly. Larger ones can be overseeded later in the process.
Making The Soil Less Acid
Ground dolomite limestone is usually applied to lawns to raise the pH to between 6.5 and 7.2. It won't kill the moss, but it will help the lawn grass compete more effectively with it. The more finely ground it is, the quicker it will work, though it can be difficult to spread evenly if it's powdery. Try the pelletized form to make the process easier. The best time to spread lime is fall since winter rains and freezing and thawing help the limestone work itself into the soil.
Only water your lawn once a week unless the weather is extremely hot and dry. Apply enough water to soak the soil to the depth of at least a foot, encouraging roots to search deeper for moisture. If the soil is compacted, use an aerator or poke holes in the soil with a garden fork. If the drainage is poor, consider getting professional help to improve it.
Dealing With Shade
You may not want to remove trees from your property, but you may be able to thin the branches to allow more sun to filter through to your lawn. You may also be able to seed a more shade tolerant variety of grass in those areas. If nothing else works, plant a ground cover instead of grass.
Re-invigorating Your Grass
Now that you have a moss free lawn, if only temporarily, and a soil with good drainage and a neutral pH, you can concentrate on helping the grass grow lush and thick. Seed any thin or bare areas with a grass seed mixture appropriate for your climate, cover with a quarter inch of loose soil or potting mix and keep moist until the seed sprouts. Fertilize regularly and mow high. Mowing too low is a common cause of lawn failure.