Once the large test chamber has slid into position, get a portal straight ahead of you and look up into the bottom of the chamber itself. There's a space on the ceiling here where you can lay a portal. Do that and then step through into the "death trap".
Once you reach the room with the turrets perched in a row to your right, zoom inside the room and get a portal on the wall for transportation beam. Now look to the wall tiles on the lower right-hand wall and fire your exit portal here. Keep moving the beam to your right and you'll eventually pick up all three turrets, allowing you to jump into the beam.
Once you've got your transportation beam going through the door and over the bottomless pit, keep your eye out for the shoot-able wall that slides into place below you. Quickly get an exit portal on here, so the beam catches you and starts carrying you backwards (away from the mashing spike plate).
Once you’re past the broken walkway (with the blue gel on it), you’ll enter a room with a large number of turrets trained on the exit. You’ll never make it by running over the walkway, so look up to your right for a broken window.
Get a portal on the ceiling here, and then set your other portal on the wall directly to your right. You’ll fall into a room with a red switch on the floor in front of you. Stand on it and set a portal under the blue gel dispenser (on the ground to your right).