The key to breaking up your clay soil is going to be the addition of organic matter in the form of dehydrated manure (cow or horse) and even sandy loam (we sell bags of ‘topsoil’ which is sandy loam). Also, the addition of Espoma Bio-tone will provide nutrients but, more important. microbes and fungi that will help digest the organic matter and convert it into loamy soil over time. HERE’S a link to more on Bio-tone. You’ll need to turn or rototill the organic matter into the soil to a depth of 8″ or so to break up the clay and blend it with the organic matter and Bio-tone.
The addition of organic matter is an ongoing process. The best soil additive will be your own homemade compost.