Watch this video and prepare to be amazed:
With remineralizing the soil, and compost, he was able to grow food with amazing yield and quality naturally. He used volcanic rock dust. Some sell and use glacial rock dust. I am conducting an experiment in my garden with different types of rock dust - results to be published here later.
A couple of other ways are growing green cover crops in the winter, especially nitrogen fixing plants like legumes. Or grow a crop with the intention of tilling it under in the spring - it's called green manure.
You could try the no-till method. This is a method of gardening or farming where tilling is kept to a minimum or not at all. The thinking behind this is to keep the soil from becoming a dust bowl again - tilled over and over until it is no longer arable.
You can read about soil biology here. You'll be a wiser gardener/farmer for it.