When it is desirable to know exactly what is happening on a multirotor, such as when flight testing a new multirotor concept or design, what measurement equipment and circuit designs are most useful and most commonly used? Are there stock products? Do they record everything on an on-board memory card like a 'flight recorder" or do they transmit the data back to a ground station for display and recording?
If you're using a flight controller running either the Cleanflight or Betaflight firmware, you can make use of the builtin "Blackbox" logging features. These firmwares rely on the flight controller to have a MicroSD card slot which you can populate or an onboard flash chip to save the flight data to.
In order to configure the flight controller to use Blackbox logging, you'll need to go into the Betaflight/Cleanflight Configurator app and follow the steps of this tutorial.
After you fly around and get back to your computer, you'll want to download the logs and view them. If you recorded to a flash chip on the flight controller, you'll need to use the Betaflight/Cleanflight Configurator app to pull them off, but you can also just pull the SD card out of the quad and put it into an SD card reader if you used the SD card slot.
Then, you can view and process the logs using the Betaflight/Cleanflight Blackbox Viewer app. Joshua Bardwell on Youtube has an excellent video playlist discussing how to analyze them, as well as Mark Spatz from UAV Tech. The UAV Tech channel is an excellent resource for this kind of technical analysis.
There are also some external logging devices that are available if you have a free UART on your flight controller.
Theres also the SparkFun OpenLog which is basically the same thing, but not quite as fast logging capability.