There may be several reasons you have moss in your lawn which include poor soils, shade, poor lawn care practices, acidic soils, etc. Look at our publication regarding moss control
You can eliminate the moss by raking and disposing of. However, if you want to get rid of it you need to correct the conditions that favor its growth. See the above publication.
Begin by testing your soil for pH and nutrient deficiencies.
Lastly, iIt can be difficult to grow grass under shade trees as there is a lot of competition for moisture and nutrients and the tree roots usually win. If the growing conditions cannot be altered, you should consider converting the areas to ornamental beds or plant a groundcover and/or shade perennials. Once established, groundcovers may require less maintenance than grass. Moss itself is considered a low maintenance groundcover and you can keep it if you like it. You can also lightly mulch (no more than 2-3 inches deep) the area under the trees out to the drip line to hold the soil. Take a look at lawn alternatives http://extension.umd.edu/hgic/topics/lawn-alternatives