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 gaming device.  In PC
Classic Doom games "Run" is typically enabled by holding
the Shift key.  In modern console ports, try holding the
Left Trigger.  Additional information follows below.

(Note: To view a video demonstration of acquiring the red
key on this level, click here.)

In early classic Doom games you needed to hold a key or
button to run instead of walk.  Some newer ports of the
game have added an "Always run" or "Auto run" option.
NOTE: If your version has an Auto-run option, and it's
currently On, then holding "Run" actually slows you.

Also, in original retail classic Doom games, players and
live monsters cannot cross paths at any height.  An active
enemy on the ground below the window may block entry
through it.

In most PC classic Doom/Doom II games, tapping the F1 key
will show a list of controls.  Following are some default
Run (aka "Sprint" or "Speed") controls in Doom II games on
a variety of platforms:

PC: Shift key
Xbox 360 or Xbox One: Left Trigger
PS3 or PS4: L2 (Left trigger)
Nintendo Switch: ZL trigger
PS1/PSOne: "Square" button
Sega Saturn: X button
Nintendo GBA: A button


To reach the red key, first 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.

Reminders: If your Doom II game has an Auto-run option and
it's currently active, then using "Run" at the same time
will actually slow you to walking speed; and, 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.

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