For large gardens... if you can locate a neighbor with a tractor... have them disc up the area to be planted. Then.. find a farm where you can purchase a couple of dump trucks of manure. Have the tractor till and mix the manure into the soil. As other posters have pointed out.. with clay.. you need to get sand, loam and other organics into the soil to break up the clay.
If you are doing a smaller kitchen garden.. you may want to look into contructing raised beds.
You can make raised beds from cinder blocks or 4x4 landscape timbers. The ideal raised bed is 3 1/2 feet wide by 18" high. They can be as long as you have room for. (Basically, you are making big planter boxes). Leave a path down the middle between boxes so you can water and weed.
Line the bottom of the planter beds with newspaper or if you can afford it.. weed cloth from your garden center. Contact you garden center and have them bring you a truck load of nice top soil and garden loam. Viola.. instant garden beds. You'll be amazed how many vegatables you can grow from 2 garden beds 10 feet long.
Plus, with raised garden beds.. you can put fences around them to keep out the deer, foxes, racoons, rabbitts.. lol. These little critters will pick you clean before you ever get one vegatable.. so there is a lot to be said for the ability to fence your beds.
I had a garden bed with beautiful tomatoes.. the blue jays picked every tomato off the vine before I could get to it. Then the deer finished the rest... it's a jungle out there...
wood and cinder block raised beds under construction