Open the two doors to the north. Go through the eastern passageway, and flip the northern switch. Enter the western building, and flip the switch. Trigger the switch in the next room, and go into the western tunnel. Flip the switch, go north, and head upstairs. Hit the switch, and head outside through the eastern doorway. Go up the rocky stairway at the north, and grab the red key. Backtrack to the red door, and open it. Go through the hallway, and press the next switch. Run on through the next door, and flip the switch.
Other points of interest
In the starting hallway, part of the western wall has a cross-shaped panel. Open it to find some clips and shells. (sector 9)
When you go up the staircase by the red door, the computer panel to the door's west will open. Quickly run back down, and enter the newly-revealed compartment to find a box of shells and a rocket. (sector 107)
After opening the red door, there is a section of wall with lights on the bottom. Open it to find a switch. (sector 154)
Flip the switch in secret #3, and return to the northwest room. Look to the western alcove to find a clip, some shells, a medikit, and a soul sphere. (sector 150)
In Boom and other related ports, the middle texture obscuring a monster storage west of where you find the red key sinks partially into the floor.
One Spectre (thing 78) on the stairway up to the red key is immobile, due to being placed squarely on a linedef separating steps.