Inductors are not the most common component these days and variable ones seem even less common. However, with a ferrite rod and some 3D printing, [drjaynes] shows how to make your own variable inductor. You can see him show the device off in the video below.
The coil itself is just some wire, but the trick is moving the ferrite core in and out of the core. The first version used some very thick wire and produced an inductor that varied from 6 to 22 microhenrys. Switching to 22 gauge wire allowed more wire on the form. That pushed the value range to 2 to 12 millihenrys.
What can you do with an inductor? For this type of inductor, you are usually interested in resonating a capacitor either for an oscillator or a filter of some kind. You see big roller variable inductors in antenna matching circuits, but it is doubtful that these inductors would be suitable for transmitting unless it was with very low power.
There are many ways to measure inductance, especially so today. The video shows an LCR meter and network analyzer. But it is easy enough to use a simple LC oscillator and measure the output with a scope or use a grid dip oscillator if you happen to have one. In the vein of making things easier, though, we really wanted to see [drjaynes] build a coil winder if he plans to make many of these.