It is usually not the rivers
Rome sits where the Etowah and the Oostanaula meet to form the Coosa, and properties on genuinely low ground near them behave the way you would expect. But most of the standing-water complaints in Floyd County are not on floodplain. They are on ordinary lots, often on high ground, and the cause has nothing to do with a river.
It is the clay. Piedmont red clay has almost no infiltration rate, which means water landing on it has two options: run off, or sit. On a lot graded by a builder to pass inspection rather than to manage a decade of storms, what it does is sit.
Start with the roof, because it is most of the water
The single largest contributor of water to a residential property is not rain landing on the yard. It is rain landing on the roof, which is a large impermeable surface funnelled into a handful of discharge points.
A two-thousand square foot roof sheds a substantial volume in an ordinary Georgia downpour, and a downspout discharging at the corner of the house puts a quarter of that into one patch of clay a few feet from the foundation. Every single time it rains.
This is why so many wet-corner and damp-crawl-space problems are solved by collecting the downspouts and piping them somewhere else. It is unglamorous, it is cheap relative to everything else on this page, and it should always be the first thing checked.
The three things that actually move water
Grading. Reshaping the surface so water runs where you want it to. This is the cheapest tool when there is somewhere for the water to go and the fall to get it there, and it is the right first answer more often than people expect.
Surface interception. Catch basins and surface drains at the low points, tied into pipe, for water that has already arrived and pooled. Useful where regrading the whole area is not practical.
Subsurface interception. A French drain: perforated pipe laid in clean stone, wrapped in filter fabric, running at a consistent fall. This is for water moving through the top layer of soil, and for the situation where the surface cannot be reshaped.
Most real properties need two of these. Almost none need only pipe.
Every pipe has to end somewhere legitimate
This is the part that unqualified drainage work gets wrong, and it is the difference between a system and a hole full of gravel.
A French drain collects water. It has to release it. That means a daylight outlet at a low point on the property, a tie-in to a storm structure where one exists and is permitted, or a stabilised discharge that does not simply relocate your problem onto the neighbour. Working out where that outfall is, and whether there is enough fall to reach it, is the actual design question. The trench is just labour.
A drain with no outfall fills up during the first storm and then does nothing for the rest of its life, and from the surface it looks identical to one that works.
Why the sod keeps dying in the same corner
Standing water kills warm-season turf faster than drought does. Roots need air, saturated clay has none, and a low spot that holds water for two days after every storm will not keep grass no matter how many times it is replaced.
The common version of this is a yard that gets regraded and resodded to hide a water problem nobody addressed. It looks solved for one season. The following summer the same corner is thin, and the year after it is bare.
The order matters and it is not negotiable: drainage, then grade, then turf. Sod over a wet spot is a wet spot with grass on it.