Moss in your yard or on the patio bricks, or even on your rooftops happens because of a number of reasons. Excessive shade (especially on the north side of your roof), poor drainage, lack of fertilizer, acid soil pH and soil compaction. In order to fix these moss problems; first determine which of these problems are occurring in your yard...probably all of them. Start by removing the existing moss by heavy raking followed by the use of a power plugger that will remove plugs of soil to allow more air circulation. If your soil has a drainage problem, you may need to add more soil mixed with sand to raise the level and help increase water to flow from the area.
Adjust the soil pH by adding lime pellets to the area and plant grass seed. No doubt this spot has a shade problem as well so get a shade-type grass seed for this area. Also consider removing low branches from nearby trees to allow more sunlight into the area. Once the grass is established and you have cut it a time or two, apply lawn fertilizers. Moss does not like fertilizer so be fooled into thinking that you might be fertilizing the moss and helping it to grow.
If you just want to fix your problem the easiest way possible, simply rake the area, apply lime pellets, over-seed with grass seed, then in a couple of weeks add fertilizer. And for the moss on your roof, get a liquid bottle of lime and spray it up onto the roof late in the evening so that there is no sun to dry out the lime spray that you just applied. I am going to try this on my outdoor carpet as moss has been a problem for many years.
Here is a twist to the moss problem, do as David Benner of Bucks County, Pennsylvania does, grow moss on purpose. That's right, David loves the stuff and says, "Why not...it doesn't need fertilizer, it smothers the weeds, it's soft to walk on, you never need to mow, the deer hate it and you do not have to water it unless it gets brown, at which case a quick watering turns it green again." And the EPA says that even though moss needs water to survive, you would only use 1% of the amount of water that it takes to water a lush lawn.