On the level "The Infernal Machine", there are two exits that lead to two different levels. One of them leads straight to "The Escher Labs" and completely skips "The Foundry" level and the second exit leads you to the secret level.
So, to find the the second exit, firstly you need to find two secrets. The first secret is located through a door located at the bottom of the staircase that is surrounded by a metal fence.

After goind through the door, jump down the pit and use a grenade launcher or the riveter (rocket launcher) on the cracked floor.
When you blow up the floor, go in it and you'll see a pipe. That is where the secret level is located, but there's a grate that blocks your way.


To open the grate, you'll need to find the second secret that is located on the left wall near the "normal" exit door.

After blowing up the wall near the door, a tunnel will appear leading you to a room full of enemies. After killing the enemies, press the button located on the other end of the room and go through the portal to your left. That will unlock the grate, all you need to do is go back to the first secret, exit through the pipe and you'll be in "The Foundry".

P.S. Sorry for my grammar.