One method to get the red key in level 15, Industrial Zone:

First, for a reference point: Look on your Automap.  In the
southern half of the map is a huge lake of crusted lava,
which spans east to west across the map, dipping south in
the middle.  In the center of the lake, against the
northern shore, is a huge light-brown building.  On the map
the building appears vaguely diamond-shaped (a diamond with
stair-stepped sides).  This building will be referred to as
"the diamond building".

To the immediate northwest of that diamond building is a
smaller, squarish building, which is surrounded by a
shallow moat of lava.  Running counter-clockwise up and
around the outside of this building are flights of stairs.
Walk all the way up the stairs to the central platform at
the top, and look for a pair of green torches.  Approach
the green torch on your right (the southern-most torch),
and put your back to it, so that you face west, towards the
center of a tall, brown, column-like structure on the west
edge of the map.

Now Run forward (use the Shift key or Run button) to run
off the platform you're on and jump across to that brown
column.  You should land on (or next to) a teleporter pad
that's on a ledge about halfway up the side of the column.

When you step on that teleporter pad, you'll re-appear on
the ledge of a building located to the north of the brown
column.  You'll be facing east.  A little ahead of you and
to the left will be a long horizontal window.  Walk forward
(east) until the center of the window is to your immediate
left.  Now Run east off this building, and with some luck
you'll land on a ledge of another building ahead of you.

When you land on the other ledge, ahead of you will be a
lion's-head switch, and a large opening into a room on your
left.  Activate the switch, then turn left and drop into
the room.  Look for a red teleporter pad on the floor in
the southeast corner of the room, and step on to it.
When you materialize at your destination, simply step off
the pad, and then step back on it again.  You'll
materialize on top of a stack of boxes, facing the red key.
Simply walk up and grab it.

Done!

PC Doom II players can access a demo of this level that
shows how to acquire the red key, by clicking here.