https://www.reddit.com/r/EliteDangerous/comments/4cfo37/google_cardboard_and_moonlight/
Here is a good step by step to get it to work if you prefer in detail. If you have a gear vr, then you need to have Cardboard Enabler App to bypass the Oculus boot. If you don't have gear VR, don't worry about buying this app.
Lens and Display Correction:
The first thing you need to do is use the reshade mod for elite dangerous to fix the lens correction and display of Elite for 3d HMD application. There is a simple 'on and off function' in one of the config files that will allow you to use it whenever. In the reddit link, there is specific notes on what you can tweak.
Headtracking:
Since moonlight does not have headtracking, I used the Headtracker app in the google store, I then enable 'transmit in background' to allow it to send the headtracking info to Freetrack software on the pc. I set up the app to have yaw-channel 1, pitch- channel 2, and Roll- Channel 0. It took a couple bit of resetting and troubleshooting for 5 minutes to calibrate... may cause nausea.
An alternative folks use is FreePie... It seems to be the standard, but wanted to avoid allowing third party app installations.
Streaming:
I use moonlight to stream elite to my phone. It only works with NVidia GPUs, I believe. You have to update Nvidia Experience software, if it's not streaming or giving you errors, change settings to update to latest beta versions. Also make sure your drivers are up-to-date.