How do I install a stone patio myself in a yard space that slopes?

Yes you will need to add draining tiles underground that carry that pooling water away from your house and the area that it keeps pooling. Then you will need to add a retaining wall to make a patio on a slope. https://karupp-did.net/plan-and-diagram-a-retaining-wall-to-diy/ I wrote a post on that exact thing. In my post I describe diagrams and how to plan the retaining wall with lots of math calculations to figure out how much stone and block you will need when ordering from the stone store. I have a link in that post where we built the retaining wall: https://karupp-did.net/building-a-retaining-wall/ We didn't have a drainage issue though so that drainage issue will be an added step for you. This drainage pipe is the type of thing you will need underground. https://www.homedepot.com/p/4-in-x-10-ft-Corex-Drain-Pipe-Perforated-4040010/100211970. Good Luck. Often times the stone store you will be getting your supplies from will give you a wealth of info as well.

I would suggest adding a drainage system before adding any stones, etc. We did this in our yard where we built steps. The area used to get realllllly wet. We graded it, added a lot of stones, and paver sand before adding in our stone steps.

Without seeing which way the low spot is, compared to the patio, compared to the house-

you might not have to do drain tile, but have the new fill dirt compacted and put turf or grass seed on it, before you start your patio project.

Youll want your patio project to be at least 2” above grade anyway and to slope about 1/2-1%.

Good luck!

I would use gravel and then polymetric sand as a base for the patio, grading it level where you plan on putting the stone. If there is a lot of water draining on the area regularly, I would add a french drain or channel drain along the edge to move the water away. This guy has a ton of videos on his page for every solution.... https://www.youtube.com/watch?v=RR3O_ZaDyv8