My soil is clay and as I work I pull out those solid lumps, let them dry off under shelter, and throw them in the incinerator when I have a fire. They need to get fairly hot , so not huge pieces, and the incinerator has good air flow and burns hotter that a simple bonfire, but it turns them into terracotta. A lot of it breaks up naturally, I thump the larger lumps with a club hammer, mixed with the ash it is a really good additive that loosens up the clay.
Like Marck says, anything organic will help, but the other thing I add is sharp sand. If you buy it as horticultural sand it is dear, as sharp sand sold for building work it is a fraction of the price, but can have salts in it depending where it is mined. I cut the top off the bags and let them fill with rainwater, then make holes in the bottom to drain them. I try to keep three or four bags going so they get more than one lot of rain through them and just add a bit every time I do something.
If you can leave a bit of land for a while rough digging and leaving the lumps to weather can improve the friability considerably, best done in Autumn, freezing seems to help.