In wet areas you have two options: install underground drainage pipe to help remove excess water or plant things tolerant of these conditions. The first option is quite expensive and not always feasible. There are quite a few plants that like wet conditions. These include bog plants such as may be found on the following web site for pond gardens and bog plants:
It also include other plants such as Louisiana iris, Buttonbush, Virginia Sweetspire and cannas. The following web site may also be helpful:
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