From this room above the fiery pit, go up a short set of stairs and you reach a room with a metal staircase. Don't bother trying to walk up these stairs, because they will fall. Just make a portal up on the ledge and another that you can walk through to get up there. Or you can just jump up to the stairs that are still there; they are low enough to jump onto.
Open the door up here (using the same button that you would use to press red buttons or pick up stuff) and go up the stairs in the next room. You will see a locked door in a mesh wall. You can't break the lock, but you can shoot a portal onto the other side to get into there. Open the door in the fenced-in area.
Now you're in a room with two big fans. Just shoot a portal onto a wall behind a fan (it doesn't matter which one.) It might take a few tries to get the portal gun to shoot between the fan blades, but it's not that hard. Then make a portal of the other color on a floor or wall in the room you're in. Once you're past the fan, shoot a portal onto the wall behind the far ledge of this room above the pit, and go up there.
Once you're up here, shoot a portal onto the highest part of the wall back here, and shoot a portal of the other color onto the floor. Continue falling through floor portals until you land on the walkway that goes over the pit.
I can't remember for sure, but I think that one end of the walkway leads to some of Aperture Science's back rooms, with a slideshow that you can watch, and some desk chairs and computers that you can play around with.
At the other end of the walkway, you reach a room with an exit sign painted in blood. Shoot a portal as high up on the wall above the blood as you can shoot, then shoot portals on the floor and fall through repeatedly until you land on the upper ledge.
Go up some stairs in this area and you eventually reach a place where there's a weighted storage cube tube with part of the glass broken. Hop in. You will automatically slide through and end up in Test Chamber 01.
Go over and stand on the red button, and shoot a portal on the wall beyond the chamber lock. Then make a portal in this room to go through into the area past the chamber lock.
Now you reach the room with the elevator, except the elevator isn't there. Jump down to the bottom of the elevator shaft.
Make a portal on the ceiling of the fenced-in area, then make a portal on the spot where you landed when you jumped down the elevator shaft. You might have to crouch to get down from where you land.
Stand on the tallest piston and shoot a portal onto the floor that you see when you reach the top. Then go back into the narrow area with the portal that you came out of earlier to get onto the top of that floor.
Now stand on the edge of the sideways piston to be pushed over to the far ledge. Look around this area to find a mesh wall. Shoot a portal on the wall beyond it, then go back across the piston to the place where the floor takes portals. Use a portal to get to the area beyond the mesh.
Once you're there, shoot a portal onto the highest part of the wall that faces the ledge above you, and create another portal to jump down to that ledge.