Finding and summoning Nightbane
In order to kill Nightbane you first need to summon him, which can be pretty tricky. The Nightbane encounter is tied to a speedrun of the Karazhan mythic dungeon, and you need to be pretty decently geared in order to make it in time.
Once you enter the instance, a timer will spawn. This is noticed by the emote saying "The strange chill of a dark presence winds through the air". This is an 8 minute timer to get to Opera, kill the boss and click on the Soul Crystal located just behind the boss encounter. Clicking on this gives you a buff called "Medich's Echo", which lasts for 6 minutes. This is your new timer, and each time you click on a new crystal, you add 5 minutes to the timer. Note that the crystal tied to Maiden is actually in front of her, so you don't need to kill her before getting the crystal.
The basic strategy is pretty much just pull as fast as possible, bring as good geared people as you can, and rush trough it.
The crystal behind Curator is the last one, and if you manage to click on this while still having the buff, you should be able to summon Nightbane. Now Medivh will have spawned Nightbane, and talking to him starts the summoning of the boss. You need to hurry to the boss room, because you only have 5 minutes before Medivh will despawn, and you won't be able to summon him. You will also get the achievement "One Night in Karazhan" upon talking to him.
Once you have summoned Nightbane, you can play it safe again, because he will not despawn as long as the instance is not reset. This means that you can take it easy, and even wipe a few times without loosing out on the loot.