Amending clay soil does not need to be difficult, but it does require some thought and consideration. Test your soil to determine what it is missing so that you can amend it accordingly. From there, select your desired method to get the needed nutrients into your soil. Finally, continue this process whenever your soil needs it. As your plants go through their life cycles, they will help to build the soil and amend it as well.
Test the pH level of your soil to determine what you need to change. (Most large home stores sell a soil test kit.) This will tell you what the nitrogen, phosphorus and potassium levels are. Depending on the results, you may want to add bone meal (which raises phosphorous), gypsum (which raises calcium and lowers sodium), lime (which raises calcium), or sulphur (which helps address excess alkalinity).
Break up the first six inches or so of your soil with a mattock. Break it up as finely as you can, so that when you amend it, the soil will be easier to mix.
Add compost and whichever mineral amendments are appropriate for your individual soil's pH. The test results will help you determine what you need to add, and in what amounts.
Allow your soil to rest for a week before you plant anything in it. This will allow the ecosystem of micro-organisms that powers your garden to return to normal. It will then be ready to help your plants grow to their full potential.