You need a slight slope to direct the water away from the house in the back and on the side.

The advice noted above is great, but if you want the backyard to be more user friendly, you'll need to terrace (step down) the slope, hold it back with sometype of retention and make yourself a decent size patio if you'd like to entertain there. The patio you currently have is way too small.

Here are a variety of backyards with sloped hillsides.

More plants means more roots to grab the water on the slope rather than grass that holds very little water.

To avoid foundation problems,follow Yardvark's advice. If possible, dirvert most water on or above slope to make it easier to manage near house.

I would definately look at terracing the slope for a lot more useable yard. You can still use the work idea from above. We had a very sloped hill next to our house the water ran straight into the basement of our house before we bought it so the walk out of 1600sq ft had never been developed not even windows. The first thing we did was dig away from the foundation and take all that material wawy to form a hill with a good retaining wall with gravel. big o and move all that water away from the house . In 13 yrs we have never had water in our now nicely finshed walk out basement .The hill that was formed from all the dirt now has a pond and lots of plantings and looks amazing . The retaining wall provided a really nice private space for outdoor dining right next to an outdoor kitchen . Think of what you can do with some terracing.

Thank you all for your advice! Yardvaark, thank you for taking the time to do the illustration. Do any of ya'll have landscape recs in Atlanta? We had one come out and quote us $5,000 and that's way out of our budget. I would want a pro to do the grading to make sure the water flows properly but after that I would definitely feel comfortable taking over the decorative aspect. Again thanks, ya'll are awesome!!

The main cost of installing a drainage system of any type is the labor. Commercial landscapers use mechanized equipment (backhoe) to dig the trench. Determining the "slope" is easy math. If you have young friends, the "ditch" can be excavated by shovel. Now add gravel. Perforated drainage pipe, the type installed around house foundations, and the screening that goes with it, are sold at Home Depot etc. You will need to provide the laborers with lots of cold beer.

Our neighbor just cut our grass. Here’s an angle from the other side if it helps get y’alls creative juices flowing 😉😬

You could benefit not only by sloping the pitch away from the house, but by installing a curving retaining wall somewhere near the toe of the slope. The scheme of catching the water in a swale you would still integrate above the wall and mildly in the patio below the wall. That's all surface drainage. You'd also need to drain from behind/within the wall, too. Watch some YouTube videos about the subject to get an idea of what it involves. Explore various retaining wall construction methods and see what might be workable you. Professionally built retaining walls tend to be expensive, so consider what you might be able to make. The wall would not need to be farther from the house than the far edge of the patio. Maybe it would be 2' or so high, so DIY is possible if you have those skills.