The entrance to Blackrock Caverns is pretty easy to find. You will want to head to Blackrock Mountain (Burning Steppes/Searing Gorge) just like you were going to go into Blackrock Spire. From the meeting stone at Blackrock Spire you will want to head up the passageway just like you were going to BRS. On the way in you may encounter a couple mobs by a bonfire. Right after the bonfire you will see some broken crates and stuff, you will want to look to your right. The entrance to Blackrock Caverns is right there. This is a pretty quick one to find and flying in Azeroth only makes it that much faster and easier.
I am not sure how I feel about this new process of finding the entrance to a dungeon before you can do it. On the plus side, if you queue in through dungeon finder, which most people do, and you die inside the dungeon you will be able to find your way back. Also if you have to meet there at least you will know where it is. On the minus side, it is kind of a waste of time while you are trying to quest.