Lime is the chemical most used to break down the clay properties. It is very effective. Follow the instructions as you can overdo it and change the pH of the soil too much. You can add compost to the soil but not manure in the first year, as there can be a chemical reaction releasing ammonia which bleaches and kills off plants. Whatever you do, don't plant potatoes where you have limed the soil. Most fruit trees and bushes prefer acidic conditions, as do some vegetables, so choose where you want to put lime.
PS Forgot to mention that clay tends to be acidic, and lime is alkali. Fruit trees like apple and pear actually do very well in clay, but I seem to recall that black cherries like a bit of lime added to the soil (but do check!)