The soil in NC is so heavy, it is hard to get much of anything to grow without tons of amendments. The traditional 'double digging' may work great in the loamy NE, but it is extremely difficult in clay.
This is the book I use to vegetable garden.
http://www.amazon.com/gp/product/1580172121/qid=1139245373/sr=2-1/ref=pd_bbs_b_2_1/104-3191258-0015949?s=books&v=glance&n=283155His raised bed system is great in smaller suburban backyards and he prefers organic methods. He tells you how to layout the garden, build the raised beds and start seeds if you plan to do that. Really everything a beginning veggie gardener needs to know.
If you are lazy, you can purchase a bed kit on the internet.
http://www.gardeners.com/Cedar-Raised-Bed/default/35-639.prd They are easy enough to build yourself, well within your abilities. This is just easier.
As far as dirt, I would clear the 3x6 areas you plan to garden on. Be sure they have full sun (at least 6 hours per day). Also, think about where shadows will go during the day. If you grow tomatoes, they will be tall and you will want to rotate them from bed to bed, so make sure there is a spot they can grow in each bed without blocking all the light from your other plants.
Once you have the grass or weed cleared. turn the soil over to about a 6-8" depth. Then you want to add amendments, stuff to break the heavy clay up with. A large grit builders sand is good (don't use small, you might end up with concrete for real), hummus, which you can buy in large cubes at the HD, and if you have a pile of leftover leaves and/or grass clippings from last year, chop up the leaves (you can just run the mower over them) and add those too. Then add a layer of chopped leaves on top to keep the weeds out.
Once you get the beds built, the easiest thing to do is call a landscaping company and have them drop of a load of garden soil. Be sure you specify garden soil, not plain topsoil. Add the soil to the beds, add more compost if you have it, and mulch.
Compost is the god of gardening, and you can make your own for free! If you don't compost already, now is a great time to start. You can compost most of your yard and kitchen waste. The gardener's supply company (link above) has a number of commercial systems available, or the book I mentioned will tell you how to build your own. I have a commercially produced worm bin inside for food scraps, and a homemade cold compost pile in the corner of my yard. You can compost kitchen waste and yard waste together, but make sure you don't attract vermin if you do it that way.
Before you plant, you will probably want to add more amendments, depending on the culture of the particular plants you pick. It is kind of like cooking; a pinch of this a dab of that some of this 'cause you have it laying around..... and viola! Beautiful food!
If you get a garden built, I will try to mail you some of my lovely tomato seedlings to plant in it.
:hi: