Clay soils are usually moist and wet, as are soils in low-lying areas, adjacent to water sources (e.g., ponds) or near down spouts. Finding plants that love and can tolerate moist soil might seem a daunting task for such areas. Fortunately, there are plenty of plants that grow well in moist soil. With some research, you can grow a variety of plants and have a beautiful garden, just like those who have loamy, well-draining soil.
Look at a hardiness zone map in a gardening book or online, such as on the United States National Arboretum website, to find the USDA plant hardiness zone in which you live. This will help you find plants that will survive your winter climates.
Peruse a list of plants that tolerate or prefer moist soil---those that have "wet feet." University extension websites, such as Purdue University, are good places to look for such information.
Determine the USDA plant hardiness zones for the plants that interest you to make sure they will grow in your zone. Again, university extension websites have pages dedicated to specific plants with this kind of information on them. In addition, search an online nursery (e.g., Nature Hills), which will list the zones where the plants are hardy.
Visit your local nursery. This is one of the best places to find plants that grow well in your area and that love moist soil. In addition, the nursery is more likely to sell plants native to your area, which often can tolerate moister soils than nonnative plants.