To successfully exit Doom II level Tricks and Traps:

One way to exit this level is simply to walk or run across
the pedestals to the exit door, before the pedestals drop
into the acid.  (Contrary to the belief of many frustrated
players, it's possible to do this... just not very easy. ;)

Fortunately there is an alternative:

Find the 8-sided "octagon room" where you first arrived on
this level.
Open the red-keyed door (on the west side of this octagonal
room), and look into the room of pedestals beyond it.
Check around to make sure there are no monsters that can
shoot/claw/bump into you at an inconvenient time.  If
possible, you may wish to save your game at this point.

Now switch to Automap mode.  On the Automap, you should see
that red-keyed doorway to the west of the arrow-shaped
player icon.  The first few pedestals beyond this doorway
should be represented as squares on the Automap.

There is an invisible tripwire, running north-south, which
bisects that empty space between the doorway and the first
pedestal.

You may want to zoom in your Automap for the next maneuver:
Slowly and carefully inch your way westward until the exact
center of the player icon (the player character's axis of
rotation) just barely crosses that invisible tripwire.  At
the instant this happens, quickly back up, away from the
pedestal, to step back into the octagon room.

Switch back to first-person view, and go through the door
on the north side of the octagon room.  Look left/west, and
you should see a teleporter booth.  (This booth is opened
by crossing that tripwire.  If the booth is not there, you
will have to go back to the pedestal and try again.)
Don't confuse this booth with one that may or may not be
open on the east wall (to your right) as you walk into this
room.

This left-side teleporter will transport you directly into
the tiny exit chamber.  Be alert for one or more monsters
that may already be in the chamber...

PC Doom II players can download demos of this level, which
show methods for accessing the exit, by clicking here.