Mulch and compost. For the vegetable garden, cover the area with wheat straw in a thick layer. Organic materials attract bugs (like roly polies) and worms that will help soften up the soil.

Welcome to the piedmont. I got here seven years ago from CA where they also have dirt. I had no idea that not everyone did. I wondered how any Carolinians could grow anything. As it turns out, clay, with help, has some advantages. It holds water extremely well and (I have heard) it rains year round. The clay also holds on to nutrients but allows plants access to them. But the clay must be amended with organic materials as esh_ga said.

It would be useful to know your ambitions, location, urban or rural, and available space. Aside from our help, you should be able to get advise from your county agricultural extension agents.

Speaking of rain and your hard clay: I thought almost everyone got significent rain last week. I would have expected your soil to have softened enough for a rototiller to break it up. Did you get any?

Digging down is way too much work, build UP your soil instead. Mound store bought top soil and mulch at least 8 inches on top of your clay. Over time the earthworms and other critters will mix it up for you.

Don't let any oak or maple leaves go to waste. In the fall, many people bag their leaves and put them out on the street. Take them home.

If you are working on your lawn just spread them across the lawn and mow over them. The more the better. The spots where you completely cover the grass wil come back best in the spring.

For the garden put the leaves in a big pile and add kitchen scraps through the winter. They will compost slowly. Once spring comes mix in your grass clipings and you will have a very hot compost pile in no time. Red clay plus a few years of compost is just about the best dirt you'll ever garden with.

Be sure and check the leaf bags you pick up off the curb before you put in your garden area. My friend use to bring me leaves as she cleaned up yards but stopped bringing the bags because of fire ants.

I wore out a set of tines on the BCS starting my garden! Depending on your space buy LOTS of organic material and till it in, I went about a foot down.

To loosen the soil up wait until after a good rain streak, it will soak in and make it softer. If dry, it is like concrete. For smaller areas you can water for several days in a row, going slow and letting it soak in not run off. Water a little, come back in a little while and do it again, let it sit and water again� Little by little the water soaks in and loosens it up.

To release some of the great nutrients look into dolomitic lime. Test your soil and add it little by little until you see good results.

Gypsy, everyone has their own recipe to augment the soil. I worked with the grey clay in the North and the red clay in the South. What worked for me is 2 part clay, 2 part mulched leaves (run over by lawn mower or leaf mulcher) 1 part peat moss (buy at lowes /home depot), 1 part sand (buy coarse), blend together in wheel barrow
(with hoe and shovel) dump in desired planting spot..7pfnlant.... .then repeat. Water thoroughly...... Mulch with needles or bark....Good Luck! It is a painfull process...but it works! When the growing season is over, lay down more Leaf mulch! Blend in for the following year.

Gypsy,
I'm with Triangle john.
This spring i bought cinderblocks at HD they weren't expensive, and I bought 5 bags of garden soil. I also bought some cow compost.
I made a nice raised bed and planted my veggies.
They grew great!
This fall I will apply mulched leaves into the bed, and I really want to plant beets the first week of September.I can't do all that work, and you don't have to. Besides,even the cinderblocks were heavy for myself and my daughter to carry and my bed is rather small, but it's permanent as long as I want it, those things are heavy.

Google "lasagna composting." It's building up, as several have suggested. It also softens several inches down into soil. Clay is rich in nutrients. Your county ag office likely does soil analysis for free, so bring a sample to see if pH etc is ok. Tilling destroys the soil structure, and in 3-4 yrs, anything organic you tilled in will be gone completely. Google "no-till gardening." Gardening here will build your character and your skills.

I agree with mccleod, what the above post calls a broadfork I think is what , up North, we call a spading fork. Even with good,decent soil I still use it to break the top 4 inches so I can haul it out and get the Mantis minitiller into the lower layer to work in rotted compost and lime.
A standard tiller will just walk all over the surface of hardpacked clay and a minitiller will with some effort dig a decent hole. It's easier to use some muscle and break the surface then go at it with the power tools.

If you're putting in your autumn leaves..not so good..they really need to be composted and crumbly before adding.