I have written a fair bit here on lawn care;

http://www.thegardenersalmanac.co.uk/Data/Lawn%20-%20Maintenance/Lawn%20-%20Maintenance.htm

I have sub-divided the data to suit different situations, so use the related links at the foot of the page to cover the lot!

Woodenshed, part depends on what pH your soil has. In low pH (acid) soils, you can add lime, and in high pH soils, you can add gypsum. Both add calcium to the soil, which causes the clay particles to clump up, rather than laying flat and blocking the drainage. Sodium in the soil also stops drainage, and gypsum will also remove most of that. You can also improve drainage with compost--or compost tea--applied at regular intervals. In fact, doing both mineral and organic remedies at the same time usually works three times as well as doing either one alone.
If the topsoil is very different in particle size than the clay, you may also need to enlist some extra earthworms to the battle. Go to the bait store, and get "red wrigglers" for areas in USDA zone 8 and warmer, and nightcrawlers for colder climates--in spring, there, of course! Their activities will gradually mix the layers, reducing the tendency of a sudden change in soil texture to stop drainage.