Get to the surface. You will see a bridge and the Combine moving its forces. Listen to Alyx and Vort and then head left.
Follow the path, and exterminate antlions standing on your way.
Don't worry about Alyx and Vort. When you get to the location you can see on the screenshot, they will join you.
As soon as you pass the wooden walls something will start to happen. Get back between those walls immediately.
It will turn out that 2 Guardians are after you. They can't hurt you, as long as you stay between the walls. However, they can throw objects at you. To kill them you will have to feed them with many bullets. Aim at head and shiny parts of their bodies.
After you kill them, head to a lift shaft. Vort will try to start up the generator but the lift will be blocked.
You will have to unblock it. Get to a ladder and climb up.
Turn right and then try to get on the green path.
Following it, you will have to remove some rocks. Use the gravity gun to do so (LMB). You will get above the lift.
Remove the rock standing on your way and move quickly to the lift. Jump on it. You will have to shake your leg pretty fast because the planks will brake soon. When you're on the lift, remove the bar blocking the hatch (LMB) and open it (RMB).
Get inside. You will see that the lever is blocked with a pickaxe. Remove it with the gravity gun (LMB).
The lift will go down. When Alyx and Vort are inside, press the button. At the top you will see a tunnel. Go inside.
Go straight. You will get to a place full of dead bodies. There are also plenty of goods. Collect it and head right. You will find a pulse rifle.
You will see a fallen bridge. If that's not enough, the vehicle you are looking for is on it.
Alyx and Vort will operate the turret. You will have to get to the door on the right that was blocked with a shield before.
Go in and up the stairs. You will get to a smashed room. You will have to move a green locker which is blocking your way.