Waterlogged garden

The bottom of our garden floods whenever we have heavy rain. Nothing major, just a few fairly large puddles but it’s annoying (particularly when the dog rolls in it). We are currently in the process of redesigning the layout of said garden, possibly including a couple of trees, possibly where the waterlogged area is.

My questions are :

What type / variety of tree or shrub would benefit from these conditions?
Do I need to dig in some sand or anything to prevent this annoying flooding?

Some water loving trees include willows, cypreses, populars, sycamores and alders.

See the link (left hand column for a more complete list)

http://www.oldandsold.com/articles25/trees-13.shtml

So why does that part of the property flood? Is it the topography (excess water unable to run off), the soil (unable percolate down), or a combination of both?

It seems to me attempting to answer the above questions will dictate the redesign of the garden and what you plan to plant there.

I believe it could be the soil. It’s a bit clay-y