This can be learned at Shattrath at the Scryer's Tier; at 43.8, 90.4, inside the building you will find a number of clickable bookcases, each of which is named after a specific profession. Click the bookcase labeled "Mining" and you will be able to interact with it as you would with a regular mining trainer.
If you are already aligned with the Aldor, you can learn Outland Mining and the associates skills from Fono at 35.87 48.54 on the Aldor Rise in Shattrath City.
And it is TERRIBLY frustrating and infuriating that Blizzard has bifurcated the Outland, Northrend and Cataclysm skills in this way. Especially with losing the ability to gain these skill points at DarkMoon Faire beyond the basic lvl 300. This character has 71 skill in Outland Mining, and the only thing I can do to gain more skill points is to "Smelt Felsteel", and that skill level is "green". "Smelt Hardened Adamantite" and "Smelt Khorium" require 75 skill in Outland Mining. So I'll probably never have enough feliron and eternium to gain another 4 skill points, when each point will require 4-6 attempts to smelt felsteel.
And frankly, who needs that much felsteel?
Outland mining for the Horde can be learned from Krugosh at Thrallmar in Hellfire Peninsula. He is at 55.47, 37.78.
[Screenshots containing UI elements are generally declined on sight, the same goes for screenshots from the modelviewer or character selection screen.]
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