In this level you are introduced to the weighted companion cube, a weighted storage cube with a heart on each side. The computer plays up the weighted companion cube as a friend whom you can trust. You need to take the cube all the way to the end of the level with you.
After receiving the weighted companion cube, use it as a step to jump onto so you can scale the wall. It's just slightly too high for you to jump over. Be sure to take the cube with you after you get up over the ledge.
Now hold the cube in front of you as you go down the first narrow hallway, because there's an energy pellet getting shot down it, which will kill you instantly if it hits you. However, the cube is invulnerable to it, so use it as a shield to get to the stairs leading down.
You'll go up some stairs to another narrow hallway. Make sure to figure out before you start going down that hallway where the high energy pellet is. I recommend holding the cube between you and the pellet shooter and walking backward down that hallway, but there are other ways you can make it down that hallway.
Now you'll reach an area where you can drop down to a lower floor, but before you do, shoot a portal onto the angled part of the wall across from the pellet containment thing. Then go back to the area with the narrow hallway, and put a portal on the wall with the black smudges from the pellet. A pellet will go into the containment thing, raising one of the platforms.
Now, before dropping down, go back to the narrow hallway area. One of the containment things has stopped shooting pellets, so you will need to make a portal where the other one is still shooting pellets. When that is done, take the cube and drop down to the lower level.
There is a side room with two red buttons, one near the entrance and one near the back. They are keeping two doors closed that block the containment thing on the back wall. You will need to put the cube on the button near the back, and then make a portal that a pellet can come through on the wall opposite of the door to this room with the buttons. When a pellet comes through, quickly step on the red button after the pellet passes by. With the cube holding down the second button, the pellet will go into containment thing, raising another platform.
Now take the cube into the other side room, where there is a pellet shooter and a containment thing, and the walls here do not take portals. So use the cube to bounce the pellet into the containment thing here.
With all platforms raised, make a portal up on the ledge and take the cube with you across the platforms. Continue on and you will reach a chamber with a red button, where the computer tells you that in order to leave, you are required to incinerate your friend the companion cube. Clearly, the cube is just a tool of the computer's cruel psychological warfare against you. But you didn't get attached to this inanimate object that the computer tried to trick you into having feelings for... right?
Put the cube on the red button and enter the room that opens up. Press the small red button to open the incinerator, then take the cube and drop it into it. The computer will open up the exit door for you. Bye-bye, weighted companion cube. :'(