There is nothing that you can do to get rid of mushrooms. Fortunately dogs and cats are not attracted to eating them, and will rarely even notice them.
If you are watering your lawn try to cut back a bit on how much water you are putting down, that may help a little bit, but more then likely it is just the weather. Even though mushrooms are a fungi, fungicides will not do anything to control them.
While I am not suggesting that you go out and eat them, most shrooms are not deadly. Turn negative into something fun, go get a field guide to mushrooms and try to identify the ones you have
growing, and instead of calling it a problem, call it your mushroom garden
and am horrified to see tons of tiny toadstools 
Not just a few... 