How to turn microphone on, on a Nikon D5200?

Please don't tell me to read the manual, it is no help AT ALL.

Actually there's information in your user manual on page 103, 104 and 210

In the cameras menu, there's an option that allows you to manually adjust the sensitivity of your cameras microphone.

Actually, you are going to find that the sound produced by the microphone and amplifier in the camera will produce pretty bad audio (this is true of all digital SLR cameras with a video feature)

You will be able to produce much better sound by doing what those who shoot videos do, use an external sound recorder like the Zoom H1. Once you start editing your video, you can then replace the crummy sound from the cameras system with the pristine sound from the external microphone

Yes it is, page 104.

http://cdn-10.nikon-cdn.com/pdf/manuals/dslr/D5200RM_NT(11)01.pdf

not pdf reader page, the manual page itself.

When you set the camera to Video mode, the microphone should automatically come on. If nothing happens, go nearer to your subject. If still none, check the manual if there's an option to turn it on. When all fails, go back to the store you bought it from. If you don't like that idea, call Nikon.

Use the Movie settings option in the shooting menu to adjust the following settings.
- Microphone: Turn the built-in or optional ME-1 stereo microphones (0104, 210)
on or off or adjust microphone sensitivity. Choose "Auto sensitivity" to adjust
sensitivity automatically, "Microphone off" to turn sound recording off; to select
microphone sensitivity manually, select "Manual sensitivity" and choose a
sensitivity.

BTW, the above is a direct quote from the manual.