The first thing you may want to do is to try and identify the reason for a spot in your yard that never seems to dry out. The most common issues are the grade of the lawn, thatch buildup, hardpan under the topsoil (as a result of construction equipment) or a high water table.
Re-grading your lawn is one solution, but can be incredibly expensive, depending upon the amount of grading that needs to be done. Hardpan, which is solidly compacted soil under the topsoil is also not easily fixed. If the area is ever dry, you need to dig up the hardpan and break it up to allow the water to drain. This may require a professional. De-thatching is the easiest fix, but if you choose to do this, make sure to aerate the soil. And finally, unfortunately, there is absolutely nothing you can do about a high water table.
By far, the easiest solution is to simply grow plants that tolerate a moist environment. There is a wide variety to choose from including evergreen trees & shrubs, flowering plants, ornamental grasses and groundcovers. If you are planting this area for the first time, you can absorb a bit of the water by mixing some organic material (mulch) into the top 3 to 6-inches of the soil. This will give your new plants the most ideal foundation for optimal growth. Tap the links below to view, by color, some of the top plants to grow in wet landscapes:
Top 5 White Flowers for Wet Landscapes
Top 5 Red Flowers for Wet Landscapes
Top 5 Green Plants for Wet Landscapes