Instructions
Grind to level 58 or 59. Anything less than that is pretty much suicidal. We are also assuming that you have been to both Stormwind and Lakeshire at least once (what Alliance player level 20 or above hasn't?)
Head to the Burning Steppes (North of Lakeshire), find Morgan's Vigil in the east and look for Helendis Riverthorn.
Accept his "Dragonkin Menace" quest and head northwest looking for dragonkin.
Return to Helendis when you are done. He will tell you to deliver a letter to Lakeshire. Fly there and deliver the letter to Magistrate Solomon in the town hall.
Accept Solomon's quest, and head to Stormwind. Highlord Bolvar Fordragon as in the battle room (top of the ramp, standing on the circle in the middle) in Stormwind Keep.
Talk to Fordragon. He will tell you to talk to Lady Prestor (standing just to your left.)
Talk to Lady Prestor. She gives you the cold shoulder, so talk to Fordragon again.
Surprise! Head back to Lakeshire and deliver another letter to Magistrate Solomon. At this point, you may want to set your Hearthstone to Lakeshire. This will save time later.
Head back up to Morgan's Vigil when you talked to Solomon again. Look for Marshall Maxwell. He will give you a quest to find someone named Ragged John.
Ride north until you hit the mountains, then west until you see a small ramp heading up to a cave. Ragged John will be at the end of the ramp. Listen to his story (it's funny!), then head back to Marshall Maxwell, then get a group of level 56+ characters together for a Blackrock Depths run.
Blackrock Mountain is in the far west of the Burning Steppes. Head up the massive ramp, in to the keep. Keep following the path until you come to a small ramp of dirt connecting the path to a large chain.
Head up the path and onto the chain. DO NOT FALL OFF! Head down the chain until you reach the small island with the meeting stone. Head down through the doors until you come out onto a stone path.
Continue following the path until you hit another chain.
Take a deep breath, then head down the chain.
Set into the wall on your right will be a hole leading into a mine area. Work your way through, avoiding the Dark Iron Dwarves (or killing them if you want.) Continue down the path until you reach the instance.
Head inside. To be continued!