I think one of the most important things about clay soil is not about the tools, but about making it diggable. It is a pleasure to dig if it is not too wet and not too dry, so knowing that point is important.
Clay is best, even after planting, when it is not exposed to the sun....ever. So thic organic mulch or
wood chips, or where I have rodent issues, I use 3/4" rock around the base of a tree, so if they dig in that zone the rocks will fall on them and fill up their hole, discouraging them, and also show me where to put more rocks.
If starting with dry clay, wet down the area by soaking it with a hose, cover with a tarp and walk away for several hours or overnight. Then go back when it's damp soil, and it digs easily.
If it's too wet in the spring, check the drainage in the area, which also may not be good for the tree
roots. Drain away too much ground
water with a
swale that can be blocked up at one end and used to hold water in a
dryer time of year.
It also helps when you dig out the hole to pile the dirt on a tarp or a piece of plywood so you can easily put it all back into the hole.
Other than that, your favorite shovel ought to do it.
An important distinction: Permaculture is not the same kind of gardening as organic gardening.
Mediterranean climate hugel trenches, fabuluous clay soil high in nutrients, self-watering containers with hugel layers, keyhole composting with low hugel raised beds, thick Back to Eden Wood chips mulch (distinguished from Bark chips), using as many native plants as possible....all drought tolerant.