Moss can grow on a lawn for several different reasons. You will not be able to stop the moss from coming back once you remove it, unless you know what conditions led to the moss's growth. For example, if your soil is found to be sour or acidic, moss can grow. You can use lime to neutralize the acid in your soil, thus preventing the moss from growing again in the future.
Kill the moss with either bleach, or an herbicide that contains the active ingredient glyphosate. When the moss dies, it will turn brown or black in color.
Rake up the dead moss and discard it. You will now have access to the soil so that you can treat it and keep the moss from returning.
Perform a soil test to make sure that your soil is acidic before you treat it with lime. According to Oregon State University, the normal pH for soil is 6.5 to 7. Anything reading below a 6 means you have acidic soil.
Place your lime in a spreader and apply it to the soil where the moss was at a rate of 40 lbs. per 1,000 sq. ft.
Reapply the lime in the spring and fall.