How to reach the exit in Doom level Mt. Erebus:

The exit is on the west side of the map, and you'll have to
step out into the lava to get there.  To get inside the
exit chamber you'll need the blue key.  If you already have
that key, skip down to "THE EXIT", below.

BLUE KEY
--------
Near the center of the map is a large, diagonally-oriented
building, with a small wooden door in its southeast wall.
At low skill levels, the blue key will be just outside of
this door; simply grab it and head for the exit.

To get the blue key at higher Skills, open that door, step
in and turn left.  Scan the middle of the southwest wall,
and look for a small candle on the floor at the base of the
wall.  Open the wall panel just behind the candle, and step
on the teleporter that's revealed.

You'll re-appear on top of a small structure located at the
north end of the map, and you'll be facing south.
Nearby and on your right are a couple of small, square
structures to the southwest: A pedestal where a chainsaw
sits, and just to the left of that, a small, square box.

Run to jump into this box, and then step on the teleporter
you'll find inside.  You'll re-appear at the northeast tip
of a 3-spoked building on the west side of the map.

Turn around and go forward and left, to the southeast spoke
of this building, where you can find the blue key.
Go to the west-side spoke and Activate the switch there,
and the tip of the northeast spoke will open up, allowing
you to leave this building.

THE EXIT
--------
Look on the Automap.  Near the west edge of the map, out in
the lava, is a tiny 6-sided structure.  Immediately north
of it is a long wall of grey stone blocks.
Look for a small open doorway in this wall, just a couple
of paces northwest from that small hexagonal structure.
Step inside and follow the short tunnel to a blue-keyed
barrier, and open it to access the exit.

Done!

PC Doom players can click here to access a demo that shows
how to find the exit on this level.