Piston room =
Shortly after climbing out of the vent, you will see a set of pistons smashing themselves against the ceiling, and the exit to the far top available through a crumbling ladder.
The center piston, however, doesn't touch the ceiling. As such, you can climb on it and ride it to the top. Shoot a portal into the corridor, then go through another portal you set at ground level.
Ceiling portal
Follow the corridor, and you should see two pistons touching the close ceiling, with almost no visible exit. However, there is a usable section to the left on a slightly higher ceiling. Put a portal there, and a portal on one of the nearby pistons and go through.
When you climb up onto the platform, you should see a marker showing the exit upward, along with a usable wall up high. Fire a portal up there, and shoot a portal on the ground, and jump through. When you fall, fire a second portal to complete a double fling.
The next corridors are obstructed with wall-to-wall pistons. To get past these obstructions, simply fire a portal on the other side, create a local portal and go through.
Pistons
You should be in a tall room filled with pistons, and you need to climb it. The fastest route up is firing a portal at the location in the screenshot, but if you can't get a clear shot, you will have to work your way up slowly.
Once you have the portal in that position, go slightly into it, and fire a portal on the opposite floor. Go through to reach a place with glass piping.
Next area
You will walk across a few glass tubes, and need to jump down. Quite quickly, you will come upon a piston that's mysteriously smashing against a wall. Fire a portal above the point it's smashing against to create the exit.
Next, you need to find a place to create your entrance. The safest location is on the lower wall where the glass tube bends, on the same side of the piston. Time your jump so that you pass through the portal as thepiston is extended.
Cross the piston, and drop down the hole.