I'm no soil scientist. I wouldn't know how to identify soil types if my life depended upon it. I couldn't recognize a deficiency by looking at a handful of soil. But even so, I observe from the results I've gotten in a variety of gardens that repeated generous applications of good compost can do miracles. Even poor draining soils can be helped by incorporating coarse chunky compost, but around here, adding generous amounts of lava cinder with coarse compost is an even better option for that type soil.
I've used all kinds of compost....hot, cold, layered, dug in, mulched. I've made well aged compost that's 6 months old, and on the other end of the scale, a chopped in a mix that only heated up for a few days before being used. They all improve soil. I've had success with my pallet grow boxes, which are just giant compost bins. I've had success creating gardens atop rock, atop even a concrete pad, by layering lots of compost. Filling containers with soil and compost also works for container gardening.
While I've read some fancy recipes for making compost, I don't see where one needs to be all that precise. Yes, there are complicated, precise recipes out there. Some gardeners are compulsive about adhering to them. But I just adhere to a 5 basic rules....
...if too wet, add dry stuff and keep out the excess rain, and aerate (via fluffing or turning but don't leave gaping air pockets)
...if too dry, add wet stuff or water. Cover the pile to keep moisture in.
...if not heating up, add a nitrogen/sugar source (grass clippings manure, urine, fresh weeds, discarded fruit, even kitchen waste if nothing else is handy)
...shoot for half green/wet/nitrogen and half dry/high carbon/low nitrogen when creating the pile
...chop everything into small pieces
Compost doesn't have to be plowed into the soil. Nor tilled in, even, although incorporating it into the top few inches will start the improvement process faster. Even if you can't till or dig, layering compost atop the ground will gradually improve the soil beneath.
And compost piles don't have to be made in order for the organic material to be useful. Basically compost is organic material that is decomposing to some degree or other. But compostable material can simply be buried into the garden in spots or in trenches. While compostable materials could be used as an uncovered mulch, much of the nitrogen will be lost by this method. Better to apply it as a layered mulch, covering the nitrogen/wet layer with something carbon/dry (example: chopped straw, dry brown lawnmower clippings, shredded tree leaves, or even a light soil covering).
I surely don't have broad experience with soil improvement. In fact, I've never worked with most soil types that are out there. But from what other gardeners have told me about their own experiences plus my own experience setting up gardens for other folks, incorporating compost into just about any soil makes dramatic improvements in the ability to grow things. About the only soil that compost doesn't improve is wet, boggy, swampy soils. But then, not too many people have tried planting a vegetable garden in a swamp, so I haven't gotten much feedback on that situation.
I have heard from blog readers who tell me they have had success growing in sand, clay, gravel, and even worn out abused soils by constantly adding compost and using mulches. And I myself have had good success turning my hydrophobic soil on my farm into hydrophilic soil capable of supporting a nice vegetable or flower garden.
I aim to add a bit of compost to the soil between each crop that I harvest. If I'm out of compost, then I'll use newly started compost as a mulch for that garden bed. One way or the other, I try to get compost added to the soil 2-4 times during the year.