Backyard soggy all around
Look up "rain gardens" for plants that can take up some of that water.
Also look up "French drains" and "Dry wells". French drains (basically gravel filled ditches with pipes) should help move the water to a Dry Well, which is basically a hole in the ground, maybe filled with gravel, or maybe a barrel or something. What these do is allow the water to get somewhere besides the surface of your lawn and then trickle into the ground below the surface.
Since this is a DIY forum, I won't suggest you "hire a pro". But my backyard can be soggy too and I'm looking into sinking a dry well somewhere to help with the drainage.