You can use any capture software available that can grab video from OpenGL games. I believe the most popular is Fraps, which is a benchmarking and recording tool. There are also alternatives such as Dxtory from ExKode and probably many others. However all these products have one thing in common. They exist is a free trial version that usually leaves an ugly watermark in the video and/or limit the length of the capture. If you know any free product, let me know.
Recording using Fraps works because both standard Android emulator and Genymotion use OpenGL, BlueStacks probably works too.
Here's how the screen looks like when using Fraps and standard emulator. I don't really like it, because on my laptop, the emulator is just painfully slow. Notice the awesome 2 frames per second displayed in top left corner.
Genymotion is much faster in my case. I can get to nice 30-40 fps easily (screenshot somehow captured rare moment when it was 60 fps). It works the same as with standard emulator. I have to mention that Genymotion includes a video recorder in the paid versions and the free version can't be used for commerical purposes.
Recording video using Fraps is very straightforward. Set the directory where you want to save the video and simply press the key that you have setup (standard is F9) to capture the video.