The computer mentions someting about momentum, but her words get garbled. There is an orange portal on a piece of wall sticking out above where you enter the chamber. You need to create a blue portal on the floor and fall through it. Then when you go through the orange portal, you'll have enough momentum to end up on the steps.
Once you go through the next chamber lock, an orange portal will appear on another wall piece above you. You'll need to use that to get beyond the gap. However, the floor and walls up here don't take portals. But you'll see if you look into the gap that the floor there is the type that takes portals, so create a blue one such that you can fall from the ledge into it. The momentum will send you across the gap.
Incidentally, if you're having trouble falling through the blue portal, go to the game's settings and make sure Portal Funneling is turned on. This option is designed to make it easier to get through portals by automatically adjusting your position.
Anyway, after going through another chamber lock, there will be a piece of wall above you like before, except that it has no portal. Instead, the floor has the orange portal this time. You can create a blue portal on the piece of wall above you. Be sure to put it way up at the top. Then, fall into the orange portal.
You won't quite make it to the top level, but the wall piece will move such that you can put another blue portal on it and fall through the same orange portal as before. Just be sure to aim carefully so you make it through the orange portal. It's best to look down while you fall.