First... yes I will... they are fungi that grow on organic material beneath the surface, second... you can't... without a great deal of work and a lot of expense... as in digging up the area and removing the organic material (such as old tree stumps and such) and repalcing the removed dirt with new... even then you would probably have limited success. Just let them grow, mow them with the lawnmower and it's done until next crop...
Clanad's right, and the more moisture the mushrooms get, the more readily their spores'll grow. Aerating your lawn is one way to allow water to sink deeper below the surface.
Also, only mow with a machine that has a grass catcher, otherwise the spores'll be spread further afield.