To improve your clay soil, add as much organic material as you can get your hands on. Loose, crumbly compost is ideal; you can dump a 4- or even a 6-inch layer on top of the clay and then turn it all over with a garden fork (flat-tined pitch fork) or a rototiller. Shredded leaves, especially if they're partially decomposed, will help, too. Adding organic matter to the heavy clay improves the soil's tilth and brings beneficial organisms onto the site. The beneficial organisms, if supported with enough organic matter, will improve the clay soil dramatically.