When you go to flip the switch that raises the barrier dropped after grabbing the yellow keycard, there is a portion of the stone wall to the west with thicker holes in it than the others. Open this wall to find a plasma rifle and (on I'm Too Young to Die and Hey, Not Too Rough only) a computer map. (sector 107) This can also be accessed from secret #2.
After flipping the switch to lower the barrier, head into the huge corridor to the west of the yellow keycard room, now revealed, and take the elevator up to the alcove with the combat armor. A portion of the southern wall is misaligned; press on this to activate a slow lift containing four boxes of rockets. (sector 389) This lift leads directly to secret #1.
In the room that opens the way to the grassy area with the lava river, open the wall with the lightning bolt on it to the south to find a backpack and a soul sphere. (sector 285)
Inside the western room of the wooden house is a portrait on the eastern wall and an armchair in the southwest. Climb on the armchair and fire at the portrait (try using the super shotgun) to reveal a secret compartment containing a megasphere. (sector 226)
On the first time you try to get to the exit, you will be teleported to the first room in the level, in front of a wall opening to reveal a very long flight of stairs. Climb all the way down these stairs to find a toxic pit with a platform on the other end holding a combat armor, a megasphere, and (on Hurt Me Plenty difficulty or above) a computer map. The platform counts as a secret. (sector 368)
One wall in secret #5 has a different texture than the rest, with lines carved in it. Lower this wall to reveal a radiation suit. (sector 369)
Getting onto the platform in secret #5 will cause a wall to lower, revealing a sewage system. In the west is a tunnel leading to a room with a switch lowering the barrier blocking the level exit. Head down the sewage tunnel until you come across a wall in the west with filth originating from the ceiling. Open this to reveal a stairway to the platform from which the imps attack you in the switch room, containing three cells and a megasphere. (sector 204)