According to Oregon State University, iron compounds act as a contact herbicide when applied to moss. They essentially burn the moss, stressing the plant to the point of death. The moss will turn brown and appear dead, just as other undesirable plants do when sprayed with a weed killer or similar product. However, iron doesn't remove or remedy the underlying problem that is supporting moss growth in the first place. And if those problems aren't fixed, the moss will return.
There are a few different iron compounds available for use by the homeowner on moss problems in the backyard. According to the University of Alaska Fairbanks Cooperative Extension Service, there are ferrous ammonium sulfate, ferrous sulfate, ferric sulfate, as well as iron chelates. These products are available in liquid and granular formations. Granular formations should be mixed with water and applied as a spray. Oregon State University recommends that 3 oz. of iron sulfate or ferrous ammonium sulfate be mixed with 5 gallons of water and sprayed over an area no larger than 1,000 square feet.
Grass that is growing on soil that can't support it will quickly yield to moss and other weeds. If the moss is extensive, kill it off, then begin a comprehensive soil improvement program before replacing the turf. Before applying the iron compounds, aerate the soil with a power rake or the proper dethatching tool. After the moss has been removed, till the soil and amend it with compost prior to planting the grass seed.
Sometimes, the problem may be that the site isn't favorable to growing grass at all. Very shady spots under trees, for example, may be better suited to a shade garden than a patch of turf. If you can increase sunlight to the ground by removing some tree branches, without damaging or stressing the tree, then increase sunlight penetration before reseeding the area.