Crawl into the vent if you want, and look around. Otherwise, go the other way and you will reach an area where the floor is blocked by several horizontal pistons. When you walk across them, they will move out of the way such that you can't walk across to the ledge beyond.
In this pit, three doors will open on a time delay. The doors each have a turret standing inside. Now, don't panic. Remember, turrets are easily disabled by making them tip over. I can't remember if the floor in here can take portals, but if not, all you have to do is make a portal on a side wall or behind the turret after the door opens, then walk through a portal to get behind or beside the turret, pick it up and tip it over. Of course, if you can make a portal on the floor, just make a portal on a high part of the wall and make a portal under each turret as its door opens.
After disabling the turrets, you'll see a grabby claw thing in the third turret room. Look above it to see a room up there. Shoot a portal there and another in this room to go up there. There is a cube tube here. Use a portal to get on top of the tube. From there, jump onto the metal ledge. An arrow drawn in blood points to a hole that you should drop down into. There is an active turret here, so wait for the hatch to open and then drop it down. Once it stops shooting like crazy, jump down to the floor.
Back up until you can see the top of the hatch that opened, and shoot a portal onto it. Then make a portal on the floor, and when you come through the portal, make another portal on the floor below you to fall through. You should make it onto the ledge.
Continue on and you find yourself in some back offices of Aperture Science. There is a door with a particle field in front of it. Go through the particle field and open the door. Press the red button, and a mechanical eye with a blue laser sight will awaken. Don't panic! It will slowly rotate until it has you in its sight. When its eye turns red, move out of the way. It will shoot a rocket through the glass, shattering it.
Go through the glass and circle around the rocket turret (staying out of its sight) until it's facing the glass on the other wall. Make the turret shoot through this pane of glass, then go through into that room. There is a door here, so go through it. But before you leave this room behind, put a portal on a wall that the rocket turret can shoot into.
Now go through the door and make your way down the hall to another door. Open it and go through, then make a portal of the other color facing the glass wall in here. Get the rocket turret to see you through the portal such that it shoots through and breaks the glass that bars your way.
Once you're through, you see a cube tube, and the words "over here" scrawled on the wall. There is a vent that you can't jump up to. A weighted storage cube would help out right now. You could just go and get a chair from the office back there, but it's a lot easier to just make the rocket turret shoot a hole in the cube tube and grab a storage cube that falls out. Put the cube below the vent, hop on, and crawl in.
At the end of this vent, there is a spinning fan. Shoot a portal onto the wall below the fan, then get out of the vent and shoot a portal somewhere that you can go through.
In this room, there is a poison pit, so be careful. Shoot a portal above the ledge that you can see beyond the poison, then use another portal to get onto there.