How to exit PC Doom II level 16, Suburbs:

First, get the red and blue keys: You need the blue key in
order to gain access to the red key, and you need the red
key to open the exit teleporter.

The exit is in the northeast corner of the map, where
you'll find a cluster of black-paneled structures.
Here, look for a wide cube that is covered in narrow,
vertical black panels.  Activate it like a switch and it
drops down momentarily.

Diagonally behind that cube is a taller column, also
covered in the same rectangular panels.  Activate it, and
it drops down.  Get on and ride up.
Face northeast towards the black walls, and step off the
column to drop down to a platform.  Turn back around to
face the column, and Activate it again.  It drops down,
and, at the same time, the walls behind you will open up.

Walk through the open walls to where you'll see a red
column ahead in the northeast corner.
The red key removes this column.  Stepping on the teleport
pad behind it will take you to level 17.

To access a quick downloadable demo showing how to exit
this level, click here.