The soil of the Victory Garden has had what all soils need, lots of organic matter added. Back in the beginning Jim Crockett and crew built the planting beds for the show in the studio parking lot.
A soil test done by a good laboratory is one part of making a good healthy soil. That gives you an indication of the nutrient balance in your soil as well as the soils pH. Along with that soil test these simple soil tests can help guide you toward a good, healthy soil,
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.
If you also spend some time with Magdoff and van Es' book "Better Soils for Better Crops" you will be able to understand better what your soil needs.

Here is a link that might be useful: Better Soils for Better Crops

We have clay soil also, although our soil is not red in color. It has taken us nearly a decade to get the garden plot transformed into soil that is easily workable. I add compost, from our compost pile, every spring. Our compost is mostly shredded tree leaves, raspberry canes, and similar yard waste. Very little nitrogen. I have never had the garden soil tested, other than pH, which is around 7.6. However, we are able to grow vegetables successfully, so I guess the soil is OK. Dolomite is a type of limestone that comtains both calcium and magnesium. But I've never used it, or any other type of lime, in our garden, because the pH is already on the high side.

mensplace -
As you noted, you could spend a fortune on "remedies".

Just add whatever cheap or free organic material you can get your hands on to help the clay get some aeration.

The discussion of too much manure concerned someone who had added astounding amounts of rodent litter to a garden plot.

I put into my garden those organic materials that are easy to obtain and free. Works really well. My advice, don't buy anything for your soil unless you are absolutely positive that you need it.

We have an occasional bonfire, and I have sprinkled some charred wood about in my garden on a whim, but since I don't recall which beds I put it on, my experiment with that isn't very informative. :-)

Marcia

I transformed virgin yellow/blue clay into what looks like coffee grounds/potting soil in one year using wood chip compost.

I could get woodchip mulch from my county composting site for free, but I cleared land and had my own trees/brush chipped (November-December).

I watered the compost and mixed in a couple of pounds of high nitrogen lawn fertilizer per cubic yard of wood chips and let it cook for a few months over winter. It was a large pile so it stayed hot all winter. I then mixed this "young" compost into the clay soil as best I could (elbow grease and a shovel since I don't have a tiller). I used about 6" layer of compost mixed into 10" of clay soil (spade depth). The first year the soil was lumpy and rough, some things grew very well (tomatoes), some things did not (onions). I mulched heavily so that the soil did not dry out, and as a result the chips broke down almost completely by the end of the season. The roots from the plants penetrated the clay clods causing them to break up. At the start of the second year the soil quality was amazing down to the depth I originally mixed the soil and I had no trouble growing anything. At this point it is a good idea for me to keep adding compost every year to maintain the soil. I have a cover crop of rye this winter hoping to break up the last of the clay clods.

You really need compost humus to build good soil. This consists of bulk partially decomposed plant fibers and chemical humics (humin and humic acid). I add a good bit of charcoal to the garden because I burn brush and quench the coals rather than letting them burn down, but this just results in charcoal lumps in the clay soil when I mix it in. Ground charcoal will act (chemically) like humics, but getting humus is alot easier than getting ground charcoal. Humus (humin, humic acid) is the chemical end product of lignin breakdown from woody material. Fad additives might have a short term benefit, but if you see a benefit it should tell you that your basic soil structure could be improved. Garden and kitchen waste compost (non-woody material) adds bulk (cellulosic) organics (but little in the way of humics), which help the soil for a couple of years until the are respired away by soil microbes. Wood chip based compost is heavy in the lignin organics (humics) as well as bulk organics, and will benefit your soil for decades. I see no reason to buy one of the "active ingredients" of good compost in a bottle (humic acid, or whatever they are calling it on the lable).

Making "bio char" wastes more energy and nutrients then you get from the end product, and burning organic matter sends more pollution into the atmosphere then does a coal fired power plant. While a dark, rich looking soil could be the result of adding organic matter, because soils with adequate levels of OM will be a rich chocolate brown color, I have seen both clay and sandy soils that looked black and had no organic matter in them.