How to find the secret exit in level 44, Suburbs, which
leads to level 58, The Mansion:

Look at your Automap.  In the southwest corner is a wide,
flattened spiral staircase.  At the top is the blue key...
you'll need this if you don't have it already.  (If you
haven't grabbed the blue key yet, be prepared for a massive
assault once you pick it up.)

Now, find the red brick building on the east side of your
map.  You'll see that there is (or was) a tall silvery door
in each of the 4 walls of that building.  Open the door on
the west wall if it hasn't been opened already.  When it's
open you'll see a solid pattern of mashed skulls filling
the doorway.  Behind this texture is the secret exit, but
there's an inner door blocking your access to it.  Here's
how to open that door:

Find the long rectangular building that's located near (and
parallel to) the top edge of your Automap, and go inside.
Once inside, you'll find a blue-keyed door that opens into
a small room.  In that room is a window, and on the left
edge of the window is a switch.

Now, you have to do the following 6 steps in order, and
very quickly, as the hidden door that you trigger now will
stay open for just a few seconds...

1. Activate the switch in the window (it may be easiest to
   do this while standing on the window ledge).

2. Run back out of this room through the blue-keyed door.
   (Remember that "Run" in PlayStation Doom games is
   typically enabled by holding down the Square button.)
   You'll see that a teleporter booth has been revealed,
   ahead of you and a little to the right.

3. Run into the teleporter.

4. You'll appear just south of that red brick building on
   the east edge of the map.  You'll be standing on a
   raised platform surrounded by four plasma rifles perched
   on short pillars.  If you didn't pick them up before
   (and you want them), get them now, and then start again
   from step 1.  (By the time you pick up the rifles, that
   hidden door will have closed again.)

5. Run to that west-side doorway in the red building.  If
   you Run straight ahead from where you teleported to, the
   exit door will be on the left side of the building, so
   Run forward a few paces and then turn right to face the
   doorway.

6. Run in.  Hit the switch you'll see in front of you, and
   you'll be off to level 58.

If you find that you didn't get to the door in time, simply
try again from step 1.  It may well take several attempts.