The usual thing with heavy clay soil is to rough dig or plough in the autumn and leave it exposed to the action of the frost over winter. This breaks the clumps apart with minimum effort. It depends where you are in the country whether you can consider winter over yet - here we have three more months to go!
Although you want big lumps of clay to break up, you don't want it so fine that it forms a crisp crust on the surface, which makes it difficult for seeds to germinate.
We found that when we had pigs to clear our veg beds, at the depth their toes went down in the mud was where a hard pan developed. This needs to be broken up to allow for better drainage, so if you rotavate you need one which goes deep. If the ground is sticky and builds up on your boots, don't work it until it dries out more.
It will take a lot of sand, but if you add that every year, plus plenty of garden compost, grit, and peat if you use it, then your soil will improve over time.
Good luck with your bees - are they hives or wild?