To find the secret exit in SNES Doom level E2M2, Refinery,
which leads to E2M6, Fortress of Mystery:

When your first appear on this level, you'll be looking
down a wide hallway, towards a large rectangular cage in
the distance.
Before you get to the secret exit, you have to activate a
hidden switch, and pick up the blue keycard:

Walk to the end of the hallway and turn left to walk around
the cage.
Behind the cage is a long wall with two doorways in it.
When facing this wall, go into the left-hand doorway.
Follow that hallway, passing the blue-keyed door on your
left.

Continue through and around this hallway until you come to
a doorway on your left, but do not enter it yet.
Turn your back to this doorway, and look at the wall in
front of you.  At the far left end of this wall is a secret
panel.  Walk up and Activate it like a switch to open it.
When the panel opens, look just inside and to the right for
a red switch.  Activate this switch to open a distant wall
that blocks access to the secret exit.

Step back out of this secret area, and turn around to face
that nearby doorway again.
Take a step through, and then turn left.  In this wall, in
the corner, is another secret panel.  Activate it like a
switch, and it rises up.

Step through, and you'll be in an oval shaped room with a
small pool of green slime in the center.
Turn right, and walk out of this room, into a small room
where you'll find a shotgun.

Continue straight out of this room, and you'll step into a
corridor.  Turn right and go down the corridor, then turn
left and go to a door that you'll see in the wall ahead.
Open it and go through to a small room, where you'll find
the blue keycard off to the right.

Now exit this room, and follow the corridor back around to
the right, then left into the small room where the shotgun
was, then straight, back into the room with the small slime
pool in the floor.

Here, go around the pool to the right, and look for a
vertical section of the wall that opens when you Activate
it.  When the wall is raised, walk through and straight
ahead, to where the hallway turns left.
Follow the hallway until you get to the blue-keyed door.

Walk through the blue-keyed door and turn right.  Follow
the corridor around to to a small, open courtyard.
At the far end of the courtyard, turn left and look for a
doorway.
The doorway leads into a darkened area crowded with 4-sided
floor-to-ceiling pillars.  Step in, and look for a doorway,
up ahead and off to the right, at the far end of this area.
The doorway leads to a rectangular platform at the edge of
a wide, indoor pool of green slime.

Step to the right-hand edge of this platform, and turn to
face the slime pool.
The slime is corrosive, so you'll want a radiation suit...
There is one located in a small chamber on the other side
of the wall to your right: Step off the platform and make a
quick U-turn around to the right, to get into that small
chamber and pick up the radiation suit.

Step back into the slime pool, and turn right.  Look for a
long, narrow tunnel that leads away from the pool.
Go down the tunnel and follow it as it turns right, leading
into another, smaller enclosed slime pool.
Walk into the center of this pool, then turn around to face
the tunnel you just came from.

To the right of the tunnel, near where you emerged into
this slime pool, you'll see a narrow passage with an exit
door at one end.

Walk into that passage, and open the door.  Go through to
the room ahead, where you'll find some ammo, and the secret
exit switch.  Activating the switch will take you to level
E2M6, Fortress of Mystery.