Q.How can I create correct yard drainage?
My backyard has slightly lower soil level in middle third of lawn area. When heavy rains come, water accumulates and stands all day. Three nearest neighbors’ yards seem slightly higher. I want to do a dry well in center and berm on at least one side. Perhaps, I need to add more plantings in low areas too?

Certified GKH Gardening Expert
Dry wells and berms sound like a good idea. You may also want to look into french drains.
As for plantings, a rain garden is a good option for yards like this. Here is more information on that:
https://www.gardeningknowhow.com/special/spaces/rain-garden-design.htm