Clay soil is not what most gardeners want to deal with. The soil is compact and sticks together in a way that makes water drainage difficult at best. Because of this, rain water tends to stand on top and run off without properly soaking in. There is little air in the soil because of its compactness, but it does have many nutrients to help plants grow. If you can break clay up to give it a looser quality, plants will benefit from the minerals contained in it.
Till up the soil as deeply as you can. To break up the soil and improve it, you want to go down as far as you can. This will bring much needed aeration to the dirt and loosen up compacted areas that are generally hard to dig.
Dump organic material and sand on the soil and till it into the ground. The sand will aid in drainage because it creates space and absorbs very little water. Organic material will also add space as well as rich nutrients. Having this material in between clay particles will keep it from sticking and clumping together as bad as before. The organic material with break down quickly, so this is only a beginning step in maintaining an enriched clay soil.
Mix compost into the soil every year. Add it at the same time as the sand and other material during the initial process and then every year thereafter. Compost doesn't break down as quickly.
Mix in added nutrients that are lacking in clay such as phosphorus and lime. These don't make their way into the dirt when spread on top, so adding them when you are mixing up the soil will get them further down where the roots of plants can benefit from them.