How do you escape the torture room in Metal Gear Solid 3

While in the cell after the torture cutscene, go to the 'cure' menu. While viewing Snake, spin him around for a while with the analog stick. After spinning him for a few seconds, exit the menu and watch Snake puke. The guard (Johnny) will come in to see if you're okay. Kill him with the knife and leave.

There's another way, too. At one point in the torture room, you can look around with L1 and see the Sorrow holding a sign with a frequency on it. Calling this frequency with the Codec will unlock the door. The code is 144.75.