How to get the red key in MINOS.WAD:

In the southwest quadrant of the map is a room with a
raised central area.
(From the middle of this room, stairways lead down in 3
directions, to blue-keyed doors to the north, east, and
west.  To the south is a wall with an elevator behind it.)

If you stand in the middle of this room and face north,
you'll see two other raised areas, one each to the
northeast and northwest.

You have to Run from the middle of the room, across the
gap, to the raised area in the northeast.  Remember that
"Run" in PC Doom games is typically enabled by holding
down the Shift key while pressing the up or down arrow.

It is recommended that you kill all the monsters in the
north end of the room (if any) before you attempt this
jump.  Make sure no living monsters are down in the gap
that you have to jump across.  (Players and live monsters
cannot cross paths at any elevation, due to the way the
game is designed.)

As an alternative, you may want to try "Strafe-Running":
using a simultaneous combination of Run plus Strafe.  (In
PC Doom games, "Strafe" is typically enabled by holding
down the Alt key.)
Strafe-Running provides a speed slightly above that of
normal Running, but moves the player character at an odd
angle.
It can take some practice to become proficient with this
maneuver.

Once you've jumped the gap and landed in the northeast
section of the room, the north and east walls of that area
will open up, releasing some monsters.
Where those two walls converged at a corner, you'll find a
narrow pillar.
Behind that pillar is the red keycard.

To read about and/or download a demo of how to access the
red key, click here.