Keep going straight. You will get to a cave. Go further and you will get to a passage going over the abyss. The Guardian will be waiting there. You will have to pass him fast.
When you do this, head towards the illuminated tunnel (A). Be fast or else you will get hit pretty badly.
When you get to the end of the tunnel, save your game and be ready, cause this is the part of the game in which you have to be quick. Turn right and try to get to another illuminated tunnel.
And then to another one.
This is the task which depends on your skills. Finally you will get to the place that you can see on the screenshot.
The way to deal with the Guardian is shown in the following film. All in all you should get to the place seen on the screenshot.
Go down and straight ahead. You will get to the room with a lift. Kill any barnacles and walk to the lift.
It will turn out that the lift is broken. If you look carefully you will notice that one of the cogwheels is missing.
Turn around and go to the right side of the cave. Open the stash you will find there.
Then get to the boxes. There's the cogwheel you need. Grab it with the gravity gun (RMB).
Take it to the lift mechanism and just put it on its place but before you do this, kill the barnacle above. Then pull the lever. Get on the platform and press the button. Wait for the vort to come down.
Follow Vort. He'll lead you to the extract. Wait until he collects it and get to the lift. When both of you are there, press the button. You will get straight to the room where Alyx is.
While Alyx is healed, you will see your "old friend" in a vision.
When Alyx is healed, you, she and vort will set off to find a working vehicle on the surface. Take the goods from a crate on your way up.
Get to a passage blocked with some planks. Remove them and walk through. The new chapter will begin.