The central lava chamber of Blackrock mountain has a central stone pillar connected to an outer ring path by large chains. The ring path is sort of tilted so one part of the ring is lower than the other.
Go to the upper part of the ring path where a large chain anchors to the outer wall. Go up a small rocky hill that attaches the chain to the path floor to get on the chain. Go up the chain and jump to a hill-like ledge that goes up along the outer wall to the right. This ledge will lead upwards, but stay to the left to get around a large rock that appears to block the path toward a a small stone balcony the just out of the outer wall above where the chain anchors to the wall. There is a gap from the side of the wall and the balcony, so you have to run and jump to the balcony. This may take some practice.
Once on the balcony a doorway leads to the instance portal for both Lower and Upper Blackrock Spire. All the accessible part from the hall is Lower Blackrock Spire except the short flight of stairs (to Upper Blackrock Spire) on the left side.
Someone please fix these instructions, if there are not quite right.