If it's not near your home - plant a willow tree. They love soil that is more wet than dry I've always been told.
How dark and how much space?
It would certainly be helpful to have the answer to 4S's questions, but ferns and mayapple (Podophyllum peltatum) are two things that come immediately to mind. If you have a lot of space and don't mind something that is thuggish in its growth habit, there's Petasites japonicus var. giganteus.
My first question would be to investigate why is it damp. Is it damp or wet--holds water? Are you in a rural area and this is just at the edge of your property? Are you in an area that is/was lower and swampy? Is this a newer house and the builder might have buried the construction trash which is now decayed and causing a low spot (this happened under our driveway!)? A low spot can be filled in or altered in such a way so as to not be a problem but first you need to know why before you start on the how.
or plant ferns,and woody plants that don't need a lot of sun and that like moisture.
There are some good questions being asked in the comments! Do you know what kind/type of soil you have?
My yard is damp and dark due to a stream entering tens of acres of undeveloped woodlands and wetlands. Dampness is a way of life down here.
Have you tried any plants yet? Sometimes it's just taking a chance to see what will grow. Some plants for wet and shady conditions you might try include - Jack in the Pulpit (http://urbanext.illinois.edu/wildflowers/directory_detail.cfm?PlantID=804&page=5) and Virginia Sweetspire (http://www.mortonarb.org/component/content/article/96/16560.html). And this site lists plants for wet and shady conditions including shrubs (http://www.hortmag.com/weekly-tips/qa/wet-shade).
I have a creek that runs through my yard and another damp (but well drained) shady area as well. Yellow flag and blue flag (irises) grow great in my wet soil. Cardinal flower and rose mallow are growing in it too. In the damp shady area, may apple, trillium, jack-in-the-pulpit, forget-me-nots, hostas, astilbe and assorted ferns are growing well.