To exit PC Doom II map 22, The Catacombs:

Look on your Automap.  In the center of it you'll see a big
raised area in some acid.  Across the top of this platform
is an arrow pointing North.  Stand on the platform, in the
center of the arrow.  Turn to face south and you'll see an
opening in the wall across the acid from you.
Through that opening you'll be looking at the exit (now you
know where it is if you didn't know before).  To get access
to it, you'll need a red key.

To access to the red key, you'll first need the blue key.
Once you have the blue key, stand on the "arrow platform"
and face northeast.  In front of you is a lift in the acid.
Jump down to the lift and Activate it, dropping it, and
then jump down into the room ahead of you.
Ahead of you will be big vertical bars dividing the room,
and to the left of those you'll see a blue door.  Open it
and Activate the switch inside.  That'll raise the bars.
Run out of this little blue closet, curving left, and let
the bars come down again behind you.  With your back
against the bars you'll see two halls or tunnels ahead of
you; Take the left-hand one.
Follow that tunnel and you'll see an opening on your left.
Drop down through that opening (there are some more bad
guys in here).  In this pit/room that you're now in you'll
see a switch, and off to the left of the switch is a raised
elevator.

Now here's a tricky part; you have to move fast...
Activate the switch.  This opens a wall to your right.  Run
through that new opening and you'll see two switches, one
to your right, one to your left.  Hit the left-hand one and
run back out where you just came from...  (The right-hand
switch is for re-opening the wall panel if it closes and
traps you)... you'll see that the lift in the room has
dropped down.  Quickly get on to it and ride it up.

Now you're next to an opening where the red key should be
sitting.  Walk into that opening and grab the red key.
Now to your right is a secret panel.  Open it and step on
the teleporter you see there.  Where you appear you'll see
another teleporter ahead of you.  Step on to that.  You'll
be back at the "arrow platform", and you should be facing
southeast as you materialize.  Jump down into the acid and
to the (southeastern) lift that you see should see in front
of you.  Activate it (dropping it) and ride it back up.
Step into the room ahead of you and curve around to your
right, and you'll see the red door.  Go through that and
the exit door is on your left...