worse lawn in Atlanta

Me and my husband are from the city Up North and so when we moved to Atlanta we knew nothing of lawn care (and still don't).  I'm so embarressed because we have the worse lawn around.  We have mushrooms, no grass, mossy, and smelly lawn.  When it rains water puddles and drains right down the center of the 'lawn' to the street, causing a brown puddle (we live on a hill).  It seems as if we have no dirt/soil either.  The roots from our 5 trees are exposed and everything I plant in it dies.  Please help!!!

Where in Atlanta are you?  If you are in a subdivision, you probably have Georgia clay with about an inch of sod.  You will need to swale and mulch the he'll out of it.

what's 'swale'?  sorry

A swale is a ditch that is perfectly level.  When rain falls, it hits the swale and then seepsnslowly into the soil.  Check out the global gardener series in YouTube, it is a few hours, but you will learn a lot about the basics of permaculture.

The mushrooms are probably a good sign. With high, frequent mowing, they shouldn't be too noticeable. Even very sparse grass will cover flaws a lot better if it's allowed to grow 4" high. I bet the patches that now have mushrooms, will be the first to develop good turf.

Some pictures of the terrain would be good and it would be good to know what kind of trees are growing on your property. Some trees produce substances to inhibit growth of other plants, e.g. elder leaves produce prussic acid when they degrade.

I lived in Atlanta for forty years.  I know grass.

You need two things, dirt and water.  Get a couple of dump trucks of topsoil (NOT subsoil) and rake it all over the lawn, right over the existing grass, not deep enough to smother it.  And figure out some way to water it or put swales in.  Grass won't grow well or not at all on Georgia Red Clay.  Too much of the Blood of Confederate Soldiers in it.

Contact your Ga Cooperative extension service run by the University of GA. They have a lot of information already on their website on lawns in GA.
Sounds like you got stuck with the normal 3 trees, 9 bushes and dying grass that they put down in newer subdivisons. If so, then take advantage of it and consider that you have a clean slate to work with. Maybe consider not even having a lawn, but instead a ground cover that needs no mowing at all. There are many to choise from.
You do need a LOT of compost to work into your soil to make it become healthy. Consider doing one area at a time until you have added 2-4 inches of compost into the different areas. Add plants one area at a time. In Atlanta GA, you can grow several warm season grasses if you want grass, including St. Augustine. Many grasses need lots of water, and there have been water restrictions in Atlanta before. Consider talking to the folks over at your County Solid Waste Department and read up on the information on Xeriscaping for your yard. Consider using lots of native plants as well. Many can be used in the Atlanta area, including edible ones like blueberries, and even strawberries for ground cover. Feed your family and the wildlife at the same time.

If you  want a lawn, (some lawn may be helpful for traffic and play area etc) one way to help change soil condtions is to core aerate the lawn. This is helpful in allowing turf roots to penetrate the hard clay. This helps to disturb the layering effect of the sod and clay. Topdressing after the Core aeration will be even better.
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If you have a lawn with plenty of sunshine go with St. Augustine.  You won't be disappointed.  It isn't so common in the ATL area but it does grow quite well with a little knowledge and care (I did it).  Second choice, Centipede, again, if you have a sunny yard.

To hell with your neighbors!  Do what is right for you or just plant Zoysia plugs.

Raking topsoil on a bare clay bank is a magic spell for making topsoil disappear. Do you need a lawn at all, can you just plant bushed and trees? A bank of forest can be left alone and you can just stay out of it. You will want to dig swales however to slow the run of water down the hillside.