The answer to nuisance puddling is installation of buried drain lines. However, in order to be able to do this you have to have somewhere acceptable to drain the unwanted water into.

What direction is the overall flow of drainage? Toward the back or toward the front?

When your yard is flooding, what is the state of the back yard neighbor's yard. (Pictures too blurry & dark to see.)

How is the shed anchored to the ground? Does it have a concrete or wood floor?

@Yardvaark the yard is sloped to drain away from the house towards the back. I think part of the problem is our yard backs up to a condo complex with a grassy area that slopes down towards our back yard. My neighbors on each side also have some flooding but not as bad as we do. The shed has a wood floor and I believe is just sitting on some wood, I can’t see any concrete.

Solving drainage isn't about what happens just in your yard, but is also about how the water can escape via the neighboring properties. If your back yard is draining toward the back lot line, it does not make sense that your back yard neighbor (condo) is draining toward your property. I think you need to do some investigation of the neighboring back yards to see where a possible outlet is. It's also possible that there once was an outlet but a neighbor made changes to their property grading which inadvertently dammed water for others.

The water in the picture looks like a small area near your back lot line, you could add some topsoil just to fill the depression that the water occupies, though this is not going to cure the problem. It will only minimize it some.

@Yardvaark I meant to come back and update. I took a walk along the part of land just behind my fence. It is all open to the condo complex. About 5 houses down from me there is a drain and there is a swell between the condos and the homes on my street. The swell disappears completely behind my property and the ones on either side of me. Would this be a something to contact the city about? I don’t want to bring in topsoil and divert more water to my neighbors on my sides.

Do you mean "swell" or "swale," as they are near opposites. It always helps to take a clear, well lit picture of the overall scene (includes surroundings) to help explain whatever you are trying to describe.

@Yardvaark

Photos are from the area behind my property and between the condo complex.

The first is from the left corner is my property and the second front the same point but to the right.

The depression (or what I believe is a “swale” ) I see going towards the drain seems to be gone along the back of my side neighbors yards and my own. The ground just slopes toward our yards from the condos. I would like to fix the flooding in my yard but would hate to just make it worse for my side neighbors if I add topsoil to my own yard.

Thank you so much for the information! I will contact the city public works and see what they tell me.