We don’t know who the [amgworkshop] wanted to listen in on, but they apparently went searching for a small FM wireless transmitter. There’s plenty of circuits around, but they wanted something smaller. The original circuit had a variable capacitor to tune the output frequency. The new design uses a fixed capacitor and a spring for an antenna. You can see the build steps in the video below, but don’t expect a lot of frequency stability or fidelity out of a single transistor transmitter.
The parts list is minimal. In addition to a coin cell holder (which serves as the construction base), you need a transistor, two resistors, three capacitors, a homemade inductor (very easy to make with some wire and a drill bit), and an electret microphone. Of course, you need a battery, too. The whole thing is potted with hot glue.
If you want a better circuit (and longer battery life) you might look at [Angelo’s] similar build. Not quite as tiny, though. There’s no shortage of other examples out there, many using different construction methods.