You have to be able to get this quest: (Horde only) Quest: Black Blood of Yogg-Saron - Thottbot: World of Warcraft
Or if you are alliance this quest: (Alliance only) Quest: The Bleeding Ore - Thottbot: World of Warcraft
EDIT: I haven't been able to find the alliance version of this quest yet but I know there must be one...
EDIT2: Found the alliance side quest finally But it's not in the same cave but should work the same...
When you have it go to The pit of Narjun in Dragonblight(the cave just outside old kingdom/anub'arakh) if you are horde. If you are alliance go to the Wintergarde Mine and start collecting thoose ore's. This will give you skillup in mining skill. Works from skill 1
You have to delete the samples/ores/quest items before they reach as stack of 10 because then you have to abandone and repick up the quest. But if you just delete the ores before they reach 10 in your bag you can keep mining there!
The only thing that is unconfirmed for me is if this really will take you up to 450 skill. If it doesn't then it's just some really easy early skill ups
And for people always demanding pictures here you go:
Oh and btw Track mining works on theese... makes it even easier
Update: Should work untill skill 420 which makes this really nice according to Ground Zero. Thanks for this info