How to get the red key in Doom II level 2, UNDERHALLS:

Short answer: You can Run across the gap, into the window
of the building where the red key is.  "Run" is enabled
different ways depending on the Doom game platform.  Common
default "Run" controls are: Shift key for computer-based
games, Square button for PlayStation Doom, and the A button
for GBA Doom II (if the Autorun option is turned off).

Look at your Automap.  At the bottom of the map, in the
southeast corner, is a large rectangular area.  There is a
wide, raised ledge running west-to-east, then north-south
in a rough "7" shape along the north and east sides of this
rectangular area.
Get on the ledge and go to the southern end.  Turn west,
and you'll see a window in a structure in front of you.
Align yourself with the center of the window, put your back
against the wall behind you, and then Run to jump through
the window.
Note that you won't be able to jump over any live monsters
on the ground in front of you.  If you bump into a monster
and fall, or miss the jump for any other reason, simply go
back and try again.
Once you're through the window, look for the stairway ahead
of you and to the right.  The red key is at the top.

Hope this helps! :)

PC Doom2 players can access a demo of this level that shows
how to get the red key, by clicking here.

Hope this helps. :)                                      

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