I am also on very heavy clay that was very compacted when I started, and I cannot second the advice to buy a mattock warmly enough. Also, get some Claybreaker (gypsum) and apply according to the instructions on the packet!
I also think that it's worth considering the time that you work the soil. If you turn it when it's really dry, you'll give yourself hell and you'll make a lot of nasty grey lumps that will then harden into rock-like balls. In the process, you could end up destroying a lot of the texture and goodness - soil is a living ecosystem, though a compacted soil is perhaps less alive than a nice rich friable one.
Instead of digging, then, I would cover the soil with a thick mulch of compost and manure and horticultural grit right now (I find that for me, grit works better than sand as sand can cause my soil to 'set', creating a cement-like, glassy surface that is a nightmare). Do not underestimate how much compost and manure you'll need - you want a nice, thick covering over each bed, not a piddly centimetre or two. And then you just leave over the summer. The dense, dark covering will lock some moisture in the soil, which will really encourage worms and other organisms to do some of the work for you. Then, in the autumn, you can try getting a spade into the soil underneath and see whether you do need to dig. You may find by then that just making a really big hole for each plant and filling it with more compost works fine.
If you do find that the soil still needs work, you can get that mattock out and get going. This would be the case if you had buried rubble, rubbish, treeroots etc that needed removing to give your plants the best chance.
I do realise this is rather boring advice. You're probably desperate to get some life, colour and plants into the garden and it does mean delaying the planting of things like trees and large shrubs for a bit, until the weather is cooler. On the upside, it'll save you a watering nightmare over the summer and a lot of work!