Place the blue portal before the stairs and jump through it to be flung out of the orange one. This will be called 'flinging yourself'. Do the same thing ahead, just from a bigger drop to ensure you make the distance.
Now that the orange portal is on the ground, you need to place the portal you come out of. Do so on the platforms above your head. Wait for them to move then fling yourself to eventually reach the exit.
Portal down to where the button is and press it. A door will open for a few seconds, shoot your portal through the door and enter the room. Use your portal to guide the pellet into the receiver.
Pick up the Dual portal device, which now shoots both portals. Press the new button and put a portal in the door that opened for a few seconds. Ride the platform back to the white wall and portal into the exit.
Now you need to use both portals yourself to fling. Get up to the highest point with the cube then jump down one floor and put it on the button. Now just fling back up to the exit.