Where do you live? Location, not zone.
What kind of grass do you have?
Have you had a soil test that tells you what kind of lime to use and how many pounds per 1,000 square feet? It could be you are using the wrong kind, too much, or not enough.

Mushrooms are not an acidity problem. I live on limestone with a soil pH about 8.0, and I have all the mushrooms I can handle. Nor are mushrooms a problem. Some of them growing in a certain pattern might indicate the possibility of a problem, but they are not a problem per se. They indicate a very healthy population of fungus in your yard. 99.99% of the time that is a good thing.

Can you take a picture on a cloudy day of the moss? Sometimes "moss" is another plant that may not be affected by a traditional moss approach. Three inches away is a good distance for identification. 20 feet away is good to get a handle on the extent of the problem.

I live in Bloomfield, NJ which is in Essex county, New Jersey.

I'm really not sure what kind of grass I have, some of it was here before I bought the house and I know I've planted some fescue and possibly one or two other mixes of sun and shade grass.

No, I have no idea how to test my soil or where to get that done. I use the lawn lime from home depo and I put it down lightly once or twice a year. As far as the mushrooms go, I don't like them on my lawn and they look ugly; for 20 years when I've seen mushrooms on my lawn I've put down a little lime and they die so I'm not sure what to think about that.

Here's a picture of a patch that started to grow back, you can see some of the brown dead moss in the upper right of the picture where it died from the moss treatment.

So I'm looking at the testing forms and prices, what's actually needed here? Is the basic test sufficient or do I need the complete package for $55?

Just the basic $25 test, which will tell you far more than you ever wanted to know about your soil.

Actually unless you are a chemist and know what soil is supposed to look like, the Logan Labs test results will be gibberish. Fortunately, morpheuspa is that guy and will help you understand it. He will tell you how much of what chemicals you need and why or why not. He will explain where to get them and when to apply. And he will be around to ask questions - all for the low, low price of admission to this forum.

Thanks for the pictures. That is a different kind of moss than I was expecting to see. Do you have a 9 iron around? It's fun to see them go way up in the air.

What is your watering regimen? How often and for how long?

Ok, I'll get on that and hopefully send it out this week.

I can't tell one moss from another but like I said I used to cut lawns all over town as a teenager and you used to see little patches on rocks and trees but not on big patches of lawn. The whole town and the next town over are covered in it, I see it all over my neighbors lawns and people have lawns with patches 3X3 feet wide and it's been getting way worse over the last couple years.

I don't water myself, just whenever it rains.

Alien invasion? :-)

Have the last few years been particularly rainy? That would do it. Even greater amounts of dew in the morning can encourage mosses. Fortunately, they're weak and easy to get rid of, so no big deal in any case.

I doubt it's an alien invasion ha ha

We haven't had any drought problems here in a few years but I haven't noticed it being overly rainy the last couple years either although hurricanes Irene and Sandy did some pretty severe damage and the whole area was waterlogged for weeks. I read an article a long while ago about acid rain and how excessive air traffic could cause an acidity problem; we have jets flying overhead constantly with air traffic to Newark Liberty, JFK and LaGuardia and smaller airports in Fairfield and Teterboro. Which is why I was wondering if moss or mushrooms were an acidity problem and that the constant jet traffic over the area could account for that.

I'm still going with aliens. They're probably tiny triffids.

Acid rain's a problem across the entire Northeast, although not nearly as bad as it was during the 1970's. Your local jet traffic isn't negatively impacting your moss problem (any more than mine does, I'm right over the incoming path to our airport, a scant three miles away).

If the soil is imbalanced, mosses can move in and make homes. They'll tolerate conditions that would kill a grass plant. Your soil test will show us what those issues are, and how to correct them.

Long-term waterlogging can cause deflocculation (plating up and falling apart) of soil, which will render the soil less capable of supporting grasses as well. The soil test should give me some indication of that in the organic matter numbers, although you can certainly start applying organic fertilizer at any time to start to fix that. It's never an issue to feed organically and boost organic material in normal soils.