Improving clayey soil isn’t an easy task, nor is it quick. It may take several years before your garden starts thriving. Instead of improving your soil, you can build raised beds.
Avoid walking on the soil whenever possible so you don’t compact it.
Perform an immersion/dispersion test: Drop a 6 mm piece of dry soil into a glass of rainwater. Don’t move the glass. If the majority of the soil first builds a halo and then disperses into the water in 24 hours your soil will benefit from adding gypsum. You need to use natural gypsum for this and go with the recommendation on the package (about 0.5 to 1 kg/sqm). This can change the soil structure from big clods to a finer texture. Don’t use gypsum if the test comes out negative.
An option is to add very sharp sand to loosen up your soil, but never use fine sand, because it turns clay into a concrete like texture.
Clayey soil is usually rich in minerals, so it doesn’t need a continuing feed of rock dust like sandy soil does.
In any case add at least 20 cm of organic matter to the entire bed. Plant green manures between your crops and dig them in.
Avoid compacting the soil, never work the soil while it is wet. Do not overwork your soil by excessive tilling. Extensive tillage stimulates microbial activity and the consumption of mass quantities of organic matter ensues. After several years of adding organic matter your clay soil becomes more friable and you have provided a deep root zone for your garden plants, you should consider reducing tillage more and more.