This isn't a quick fix, but if you have areas where you simply cannot garden due to the heavy clay soil, Gypsum (aka calcium sulfate) can improve the soil structure. There's no need to dig or till the gypsum in. Just add it to the top of the clay soil. The Gypsum will break up the clay on a molecular level, allowing water to permeate through. It's best to apply several applications (over a year or more) before you add your other amendments and finally begin your new garden. We've done this and I think it's worth the time. Gypsum can also be used to remove sodium from saline soils.