Since the caption on the photo says that it is a new home, I would suggest that you just live with it for a year to see what it actually does and how wet it is for how long. In spring, melted snow combined with rain and in some areas some frost in the ground as well as your soil texture will make for damp spots that may dry out fairly quickly once the melt has seeped into the ground and the plants get leaves and begin using water. You may also find that there are native plants there already that are perennial that die back to the ground in winter. Once you have a handle on what it actually looks like over the course of this early spring and your growing season then you can start to think about what if anything you want to do with it.

For this season:

- get a soil test done for texture, pH, and nutrients so that you have some idea of what your soil is like. This will influence what plants might be happy there eventually.

- Find out what zone you are in. Again, this will help determine what plants might be happy where you are. http://www.plantmaps.com/interactive-michigan-2012-usda-plant-zone-hardiness-map.php

- Take a photo once a week of this spot. That way you will have a record of how it changes over the course of the year, and not have to guesstimate. It will tell you not only about moisture, but also light levels and what plants are there currently. Light levels and moisture will also give you an idea of what plants might do well here.

- Do research on sources: What places in your area sell plants and of what type; for instance do they have any native plants or only ones bred for garden use? Are there sources of free compost or mulch in your area such as a farm with composted manure or municipal compost or a dump site for the chips generated by the power company when they trim back lines? Does anyone deliver mulch in bulk?

- Look for areas that resemble yours in others' yards or in demonstration gardens, nurseries or an arboretum. Take photos of whole plants and close-ups and get them IDed on the Name that Plant forum here on GW if they don't have labels which will give you a palette of plant material that might work well in your setting.

- Get the trees there IDed. (Again, good photos of the entire tree and closeup of twigs should be enough to post of the Name that Plant forum.) Some trees are better at sharing space than others.

- Think about what you want from this area: a place for kids to build forts, a woodland garden, an expanse of unblemished lawn, etc.

- Are there deer and do they often create issues in folks' yards when they eat plants?

What, if anything you decide to do with this area will depend on a whole range of factors, not just earliest spring moisture levels, so rather than doing something fast that is doomed to fail, it will help to go into the process with as much information as possible so that you aren't simply throwing away money. It isn't a quick fix type of issue.

How extensive is the problem? What water we see shows up in the treed area. Are the "usable" parts of the yard, closer to the house, affected as well? Or to a lesser degree?

Try to determine, and share, the cause. Is the water in a drainage path? Is it generally moving through the property but remaining in low spots once the flow has stopped? Or are these low spots that are not in a drainage path?

If you could adjust grade to make water flow from the low spots, where would it go? Would it be able to leave your property or is your's the lowest lot in the area? Are you able to obtain any topographical information for your area?

In general, there is no practical way to do normal grading in a forest of trees. It may be possible to do some filling of low spots, but if the land is flat, doing this may cure standing water, not the overall boggy quality of the land.

How are you wanting to use the affected land?

Both of the answers given so far are good even though they don't give you a definitive answer. You do need to see how this area looks over the course of a year to know how best to treat it. There are too many trees, but you should not just cut them down without knowing what you are removing. In my area developers tend to clear out everything except the oaks. They remove a lot of juniper which is good, but they also remove rare and desirable native trees and shrubs. When you know what you have you can make a better decision on what to remove.