I have an area that I spray Roundup on every once in awhile. The result is no weeds and all moss. Moss transplants very well this time of year in case you want to fill in some blank spots. It's a little cold for Roundup to be very effective now. Mike

Mushrooms are the fruiting bodies of enormous networks of fungi under the soil. They're actually a good thing, indicating that the soil is pretty healthy. You want good fungi down there as they do plenty of jobs for you, like aerating and processing organic material into plant food. You can pick them if you like, the only thing you're doing is removing the fruit from the tree, so to speak. For most mushrooms, I tend to simply ignore them.

Fungi are a fact of life. There are over 100,000 microbial species in your soil of which a very large fraction are fungi. As gardengal said, you will never be free of them and you don't want to be. Whether they are creating mushrooms is something else. You can minimize the mushrooms by proper watering. Watering: Deep and infrequent is the mantra for watering. This is for all turf grass all over the place. Deep means 1 inch all at one time. Put some cat food or tuna cans around the yard, and time how long it takes your sprinkler(s) to fill all the cans. Memorize that time. That will be the time you water from now on. My hose, sprinkler and water pressure takes 8 full hours to fill the cans. Your time will likely be less. I like gentle watering. As for watering frequency, that depends on the daytime air temperature. With temps in the 90s, deep water once per week. With temps in the 80s, deep water once every 2 weeks. With temps in the 70s, deep water once every 3 weeks. With temps below 70, deep water once a month. Note that you have to keep up with quickly changing temps in the spring and fall. This deep and infrequent schedule works in Phoenix and in Vermont, so it should work for you. The reason for deep and infrequent is to grow deeper, more drought resistant roots and to allow the soil to dry completely at the surface for several days before watering again. If it rains, reset your calendar to account for the rainfall.

Same here for us - the wet season. Moss is colouring up rocks, logs and tree trunks. Fungus is sprouting up out of everything. And new growth in ferns is covering over the old ratty looking fronds.