If you have a mixture of grass and moss, I've found that the best way to keep the moss from taking over is to rake out the heavier moss areas and then fertilize the grass. The grass will shade out the moss eventually, as long as you keep the grass well fed and watered (and mow it high). If the soil is acid, it also helps to lime it.
To really limit the growth of moss, you need a sunny, well drained site with a pH neutral or on the alkaline side...based on my experience & reading. My question is, if that is not what you got - WHY BOTHER? I love my mossy-shady areas. Low maintenance, lovely colours. I encourage different species & even deliberately "plant" moss to help avoid weeds in corners. the Japanese do wonderful things with moss. I recognize that it does not stand-up well to foot traffic, but the grandchildren tend to play in the sun anyway. Details on my moss planting technique are available on request....LOL.
