Very slowly.
You either do it by rotavating or manually breaking up the clay - and then by buying tons of grit and manure and adding it into your rotavated area.

Louise is right - addition of humus rich materials such as composted manure, soil conditioning compost from the garden centre or local recycling centre, or your own garden compost, spent mushroom compost, leaf mould, anything you can get hold of like that, and add as much as possible, repeating with some every year at least. Horticultural grit in big bags is also very useful.

Adding calcium to the soil, in the form of lime, gypsum, or bone meal, will cause the clay particles to stick together in sand-sized clumps--a process called "flocculation". That works even better in the presence of organic matter. Magnesium, in the form of Epsom salts or dolomite, has a similar effect, but an overdose is more damaging to plants.

I've used gypsum in autumn on unplanted, newly dug ground, but I thought it couldn't be used near plant roots, Tugbrethil, is that the case?

No, outside of its physical action, gypsum (not plaster of Paris, mind) is quite neutral. Whole, well vegetated islands in the Mediterranean are composed of it.