Sand topdressing used in combination with core aeration is a good way to increase soil drainage. Sand topdressing is a great way to level your lawn. Sand won't compact in the same way other soils types will.
*Critical- if you put sand down, do not put soil over it. Coarse material is ok over fine, but coarse material covered by fine is no good. Clay has the finest particles and sand is the most coarse.
Compost topdressing is a great way to organically amend your soil. It increases the health of your lawn by increasing micronutrients and microorganisms. It will help your soil hold more moisture and hold onto nutrients. It can be used to increase the drainage of clay soils.