Follow the straightforward path past the map and the emancipation grid. Up ahead there is some repulsion gel in the pit. Drop into the pit and the repulsion gel will make you bounce. Use the gel to bounce over to the other side.
Over here, turn around and look up to see a white wall to the right. Put a portal there, and another one on a nearby wall. Go through. From this upper ledge, jump onto the repulsion gel to reach the ledge with the (currently locked) exit door. Press the small button near the exit to make a box fall from the ceiling.
Drop down and pick up the box. Carry it while bouncing over the repulsion gel and going through the portal on the other side. Put the box on the red button, then jump onto the repulsion gel to reach the exit door. Go through.
Above the sign that says "next test chamber this way" there is a white wall above the ledge (back up if you can't see it). Put a portal there. Then go left from the "next test chamber this way" sign and turn left at the end to find another white wall. Make a portal there of the opposite color and go through.
There's an office if you go to the right, but there are no secrets there, so go left from the portal that you came out of. At the end of the walkway jump down to the stairs. Turn left to go to the next test chamber.