1) Complete the quest "Fate of the Nightborne"
2) Be exalted with The Nightfallen. Here's a guide on how to farm rep with The Nightfallen. Use this if you are not already exalted!
The quest you need to complete is the last in the Suramar quest chain, so you basically need to complete the entire storyline in that zone. This includes all quests from 7.0 and 7.1, which adds up to a pretty long chain.
The mount itself is rewarded for completing the quest, but as said above, you need to be exalted with the Nightfallen in order to use the mount. The requirement for the reputation seems to be tied with actually learning the mount, so it's most likely that you can use it on any character after you obtain and learn it with your main.
Completing this Nightfallen quest line is a pretty time-consuming process, and by playing every week you will be able to complete the entire patch 7.1 quest chain in 9 weeks. This is due to the fact that the quests are gated, so you need to wait until next week reset before you can progress on the chain.
|Arcanist's Manasaber- here from the Mount Journal.|