From StrategyWiki, the free strategy guide and walkthrough wiki

Chamber 14 involves more momentum puzzles, as well as the puzzle of how to bring an energy pellet a long distance, around several corners.

The first challenge is to get hold of a cube to put on a button so that a door can be opened. This may sound straightforward, but the cube is on top of an unclimbable raised platform.

[edit] Getting the cube

This is a momentum puzzle, as indicated by the fact that the stairs to the pellet receiver area retract once you're up there. Place the first portal at the base of the raised area, making sure to angle it perpendicular to the raised area (this should make mid-air reorientation so you can land on the area easier). Place another portal at the bottom of the pit formed when the stairs retracted, and fall into it. You should come out of the portal end by the raised platform, and have enough time to manoeuvre yourself onto it. It might take several goes if the portals are angled so that your not facing the raised area when you exit, but after a few goes you should get the hang of it.

Once you're on top of the raised area, you can pick up the cube and take it down to the button, thus opening the door.

[edit] Getting the pellet

The door leads around a corridor to a room filled with sludge and some platforms which periodically go up and down into the sludge. On the other side of the room is a small antechamber with a pellet launcher; either use the platforms or a portal to get to the room.

Once in the room, place a blue portal over the scorch mark on the wall, letting the pellet through. While making sure not to hit the pellet (which causes instant death), follow the pellet through the portal (if appropriate) with the aim of returning to the pellet receiver at the other end of the map.

At the pellet receiver, simply place an orange portal on the red spot above it – letting a pellet into it – and ride the lift below to the chamberlock.

Very, very good. A complimentary victory lift has been activated in the main chamber.

—GLaDOS