One of the best things you can do when working with clay soil is to add lots of organic matter in the form of compost. This loosens the soil and helps to improve drainage. Avoid working the soil when it is wet, because that can destroy the soil structure and make your clay soil turn into adobe bricks!
Native plants are good bets to adapt to clay soil because they have been growing in it for many years. There are also many cultivated plants such as hosta and liriope that grow quite well in clay soil with adequate moisture.