I live in Virginia and we have a nice heavy clay soil. In many locations it is very fertile and provides a good base for garden plants BUT it has many challenges that limit the productive capacity of the new garden(or old gardens still rooted in clay).
When I play ( and it is fun) in the garden and plan my future fun I do soil prep and soil improvement in the fall and during the season as crops are harvested and even as they grow.
Now first thing to address- I am a fan of building the soil WITHOUT tilling or turning the soil. There is plenty of debate on this. If you choose the till and add to the soil that way it will work as well.
I add the improvements to the soil and they get worked in by weather and worms or by me as crops are planted. I also like to use grass clippings and leaves as weed barriers around the plants in the garden. These break down and add organic material to the soil. Leaves add carbon and grass adds nitrogen ( much simplified) . These items can also be composted and when aged properly can be worked into the top layers and added to plants during planting or after the fact.
One of the great side effects of added organic material is the enticement of worms and microorganism to join us in the garden. As they enjoy the grass and leaves and compost and manure they enrich the soil, add channels for water and air to flow to the roots. More on Worms and composting with worms later( vermicomposting) .
Some video information:
This video has a discussion of browns vs. Greens. Simply put browns are compostables loaded with carbon (leaves, wood chips, mulch, paper, cardboard) Greens are loaded with nitrogen( grass, kitchen scraps even manure). When they both breakdown the compost and the soil is balanced nutritionally for plant use. He is layering to build a new garden bed but the same idea works when building a compost pile .
A few videos on composting.
A quick HOW TO:
New garden plot make a “lasagna” of cardboard or newspaper,grass, leaves, manure, compost , wood chips and repeat. If you want to use this new plot/ bed right away you can add some bagged topsoil to plant the seeds or seedlings. If this bed is for,next season/spring you can build it up with layers and let the winter work it down and plant in it next spring.
Exiting garden bed/plot Add your amendments to the soil as you harvest in the fall or as you plant in the spring. Many can be added during the season. See the reference to leaves and grass as weed barriers.