Poor drainage usually means that the soil particles are small and compacted. Clay soils have very fine particles and retain water. Compacted soils have poor structure with little air in the soil and so the water cannot penetrate.
The remedy for poor drainage in soil is to amend the soil to improve its texture. Add organic matter such as compost and mix in to a depth of about 4 to 6 inches. This is an ongoing process, and it will take time and repeated applications of organic matter.