Proper drainage can be a problem for some plant selections in the landscape. There are a few things that can help a plant grow when this condition exists. Amending the soil or diverting the water or raising the area to be planted are the most common ways.
If you have heavy clay soil in the yard it might be a good idea to plant the ball up out of the ground and berm around it with good soil. Think of digging a hole that is more like a dish than a teacup. Make it wider and not as deep. Then add soil to it bringing the soil up in a mound to raise the plant and give it a wider, better area that will drain faster around the roots.
If it is appropriate to create a berm area for several plants to grow, this is another option. It can also be an interesting feature in your landscape. Just add a foot or more soil to the planting area and then plant in the soil that was added to the bed area.
Choosing plants that will tolerate the soil it will grow in is the best rout. A wetter soil is good for Dogwood, Willows and Alders to mention a few. Check the criteria for the plants before making a choice. The same goes when using plants that require a dryer soil.
Possibly even think of a rain garden to pull surface water away from an area allowing the soil to dry out faster after a rain by giving a place for the water to go. This could be possible in many cases.
Proper grading for drainage is always the first step.