Hi John, thank you for the suggestion of adding my location and gardening zone! I am in central Missouri not so far from you I guess. Thank you for your reply I will try planting Daikon Radish and other plants that can help.
Hi Chris, thank you for your suggestion of using a broad fork. I added lots of wood chips last summer and for a while I noticed strange unicellular 'stuff' and googled it and figured it's called 'dog vomits' or something like that...yuk...and that is supposed to digest woody material. I am not sure if that is a good thing or not. I will try with rock dust and thank you for Bryant Redhawk post link. I want to create a garden with perennials, flowers and vegetables.
Hi Gilbert, thank you for your answer, I am not sure I know how to answer to your question about the structure of my soil. I can tell you that the spot where I want to create a garden was completely filled with oak trees and that I got rid of something like 30-40 of them. And then I used all the wood chips to cover the soil. So I guess is a soil that has never been used for gardening and shouldn't have too much compaction since it was not possible to drive on it or things like that.
Thank you guys for being so helpful!