After you and Wheatley discover GlaDOS's inactive remains, you end up in the incinerator.
Receive the Dual Portal Gun
Walk across the metal grating to safely cross the fiery pit. There will be some metal ceiling pieces in your way, but they will move. You will see some turrets sliding down near a gap in the metal grating. Jump across, then drop down to the floor below and continue walking straight ahead.
The dual portal gun is ahead under some platforms. GlaDOS will obligingly lift the platforms for you. Walk onto the portal gun to pick it up. You can now shoot blue portals with the left mouse button and orange portals with the right mouse button.
Shoot a portal onto the wall up ahead, then shoot a portal of the other color onto a nearby wall. Walk through to reach the testing area up ahead. There is a piece of metal blocking your way, but just create a portal beyond it and a portal of the other color near you, and walk through it.
Continue on your way. You will see a testing area up above, and GlaDOS will lower a wall piece for you. Shoot a portal onto it, then a portal of the other color onto a wall near you, and walk through it.
Drop down the nearby ledge and keep going. There is an area above you. Shoot a portal onto the wall up there, then shoot a portal of the other color onto a wall nearby, and walk through.
Turn around until you see some broken windows across the way. Use portals to reach that area. Then go into the corridor next to the wall camera. The Test Chamber 19 sign will light up, and up ahead GlaDOS will move some platforms out of the way for you and open the door. Go through, walk through the particle field and down into the elevator area. Take the elevator down to the next area.