My "soil" is more on the clay side...?

I'm thinking of growing food in my back yard, and I was taking a look at my "soil." It was vary clay...ey. I don't have money to spend on fertilizers or new soil, so I want to try to amend the soil I have. The only problem is that the "soil" is full of rocks. How can I easily de-rock it, or do I even have to?I was going to try to amend the soil with compost. Will this fix the problem? I live in AZ if that helps.