As I believe I may have mentioned, I upgraded my tractor for a bigger machine with a backhoe. I've spent a couple of weekends figuring out how to use it.
I believe they call it a backhoe because the digging motion is toward the operator, which is the opposite of how humans dig with a shovel. Interestingly, it is exactly how humans dig with their hands, and how dogs and other digging mammals use their paws.
The machine has four motions. First, the whole apparatus moves side to side. That's just to locate the shovel, it doesn't contribute to the digging action. Then, the apparatus moves up and down at what you might call the shoulder. Apparently that's called the dipstick motion. It has an elbow, which flexes in and out, and then the shovel, which curls at the wrist. The basic technique is to get the shovel approximately vertical at the point of entry into the ground, which you do by manipulating the elbow and the wrist. Then you use the dipstick motion to push it into the ground. It won't go any deeper than the fingers on the bucket, but when you curl the bucket toward you, that pulls it into the ground and if all goes well, gets you a full scoop. Then up pull up on the dipstick to lift it out of the ground, swing to the side, and dump it.
That's simple enough but digging out stumps is a more profound skill. I expect those big industrial machines you see at the highway construction projects can just rip stumps out of the ground, but for my machine, a decent size stump is a project. You can't break the roots too close to the stump -- you have to dig all around it far enough away that the roots are thing enough for the machine to get through. It takes a bit of exploration and you have to keep moving the tractor to get various angles at the stump. But once it starts to move, even a little bit, you're getting close. You just have to find the last couple of roots that are holding it, and finally it pops out.
Species differ a lot. Even quite a small beech stump is tough because they have dense, sprawling root masses. With oaks, there are a few major roots. If you can find and break all but one, you can pull out the stump. With beech species, you have to excavate the Panama Canal. The interesting question is why these two kinds of trees, which pretty much share a habitat, have evolved such different strategies for keeping themselves in the ground.
Anyway, I've pretty much figured it out. Now I'm going to open up my clearing a bit, do some landscaping, and build stone walls. Meanwhile, mowing what I already have will get a lot easier.