You will most likely find that the soil under the concrete slab is much different then what you see next to it. If the slab was properly installed it should lay on several inches of crushed stone, to improve drainage so the concrete would not heave in the event moisture accumulated there and froze. Depending on the thickness of the slab and the crushed stone under it you may well end up with a hole a foot deep that you would need to fill. Usually fairly large amounts of compost would be a good start at making soil, except here you would not, after removing the concrete and base, have any soil to speak of. The only people I have seen that get enough organic matter together to make a compost pile that large are the landscape workers that clean up other peoples yards.
Some materials are higher in Nitrogen then others, reflected in the C:N (Carbon to Nitrogen) ratio, so a good mix of material that results in a C:N ratio of about 30 to 1 (30 parts carbon to 1 part Nitrogen) is what you want to aim for and if your material is close to that, and has just enough and not too much moisture, it will heat up (the bacteria that are digesting this stuff will be working and generating heat). Many people do turn their compost and if done at the right time they will often see a spike in temperature afterwards indicating that the bacteria are again very busy digesting more material.

Here is a link that might be useful: Online Composting tutorial

The wood chips will heat up for a while as the bark, twigs, and leaves are digested but the pile will take a very long time to fully compost. This pile would be great for mulching your garden but not much good for making compost in a hurry.

Your other materials you have available sound great though for cranking out compost quickly.

It sounds like you have all browns, and no greens. Consequently you won't get very much heating, if any. So it will be a cold pile, and will take much longer to decompose. If you build that pile in the fall, it won't cook over the cold winter, but should start to break down next spring.

Add some green grass clippings to the pile and sprinkle dried blood on it to add nitrogen to help heat it up.

I use mostly dried leaves in the fall, and I don't worry too much about a perfect compost pile. You could also add peat moss to your soil to help tilth and water retention.

Enjoy, and good luck.

Thank you for the replies! They're all very helpful.

Kimmsr, I guess my patio wasn't "properly installed." It has several large cracks, and I broke a piece out in the middle to see how deep it goes: it's 4" of concrete with plain dirt underneath. I think it was a quick amateur job.

Mister Potato Head, I'll ask around and see if I can get some grass clippings. The page on coffee grounds did note that chemically speaking, they're classed as "greens" even though they're brown, so that should help some.

Any idea how much stuff I should try to pile up?

If this is a slab that is 4 inches thick and all that is below is some kind of soil then remove the concrete and dig into that soil under it and look closely at that soil to determine
1. how much organic matter is there.
2. how well that will drain.
3. how well that soil will retain moisture.
4. what the tilth of that soil is.
5. what kind of life is in that soil.
These simple soil tests can help find that information,
1) Structure. From that soil sample put enough of the rest to make a 4 inch level in a clear 1 quart jar, with a tight fitting lid. Fill that jar with water and replace the lid, tightly. Shake the jar vigorously and then let it stand for 24 hours. Your soil will settle out according to soil particle size and weight. A good loam will have about 1-3/4 inch (about 45%) of sand on the bottom. about 1 inch (about 25%) of silt next, about 1 inch (25%) of clay above that, and about 1/4 inch (about 5%) of organic matter on the top.

2) Drainage. Dig a hole 1 foot square and 1 foot deep and fill that with water. After that water drains away refill the hole with more water and time how long it takes that to drain away. Anything less than 2 hours and your soil drains too quickly and needs more organic matter to slow that drainage down. Anything over 6 hours and the soil drains too slowly and needs lots of organic matter to speed it up.

3) Tilth. Take a handful of your slightly damp soil and squeeze it tightly. When the pressure is released the soil should hold together in that clump, but when poked with a finger that clump should fall apart.

4) Smell. What does your soil smell like? A pleasant, rich earthy odor? Putrid, offensive, repugnant odor? The more organic matter in your soil the more active the soil bacteria will be and the nicer your soil will smell.

5) Life. How many earthworms per shovel full were there? 5 or more indicates a pretty healthy soil. Fewer than 5, according to the Natural Resources Conservation Service, indicates a soil that is not healthy.

and can guide you in determining what you need do to make that into a good, healthy soil. You want between 5 and 8 percent organic matter in any soil that is used to grow plants.

I'd pull up the concrete this fall and build the giant compost heap on top of your future garden. The worms will begin tilling in the compost immediately. In fact, you could do a lasagne type bed, with layers of soil in between the compost ingredients. Plants can go into pockets of added soil embedded in the bed. This avoids digging the clay right away - you could wait a season to do that and it would soften up some.

As for the size of your pile, if you're going to make it separately and till it in, figure that compost will shrink 5 to 10 times during decomposition, figure 4 to 6" (maybe) as an initial application, and back-calculate from there to estimate your required pile size.

It seems like OP is focused on tilling in OM as the only method of improving the soil. There are more techniques.

First of all, he needs to get the soil tested. Then add amendments to the surface. If it is not going to be planted in crops, then it should be planted in a cover crop, a green manure. I don't think I would bother tilling anything into the soil in an attempt to improve its tilth unless OP is going to till in either peat moss or a lot of commercial finished compost.

What I would do is; clear the ground, test it, amend it with organic amendments, fertilize it with an organic lawn food, and till the very top surface enough to plant a cover crop. Make a compost pile right away. In the fall, if the compost has made enough progress, I'd spread the unfinished compost in a 2-3" layer over the garden bed and cover that with a mulch such as grass clippings.

By spring, that should be raring to go. It will still need a constant supply of compost and mulch, but it should be productive soil.

Maybe I am just frugal, but if the concrete is broke in to chunks in a way that you can use the bigger pieces as sides, you might be able to build a bunker style compost bin. At least to start you out until you can build something more aesthetically pleasing.
My soil is clay as well, but adding compost has made all the difference. Even my grass is on par with my neighbor across the street, and he uses commercial Fertilizer 5-6 times a year. The month he misses fertilizing, it is clearly evident because his grass is so dependent on it that it looks terrible. I am down to using some turf builder in the fall and some 10-10-10 in the spring and am hoping in the next couple years of weening off those too.

Thanks for all of the excellent experience sharing here!

If you have time, please consider helping out a newbie with a similar situation. You can check out my post here:

http://forums.gardenweb.com/forums/load/ohioval/msg0920035213984.html

Well probably whatever the original poster was going to do has been done. But to throw in my advice, pull up the concrete ASAP. Pile all the organic materials you can where it was, if it is just dirt underneath the concrete. I wouldn't worry about the proportion of ingredients, just pile them up, the more the better. Be sure to put in your own vegie and fruit peelings, egg shells, etc. By the spring it will be great stuff. If you really think the browns are way too high, try to get some horse or cow manure in there, or get old produce from a farmer's market or grocery store, whatever you can think of. I wouldn't buy a gosh darned thing when there is so much organic material that other people fling out all the time.

I make a lot of lasagna beds, you don't have to wait long to plant at all. Plants are happy to grow in leaves and coffee grounds and manure and so on.

Marcia

neatlyfolded, the best way to get your questions answered here is to start a new thread rather than tack onto someone elses.