Follow Alyx and you will get to her father.
After meeting Alyx's father follow him to the silo. It will turn out that there are some problems with "pests". You will have to take care of it.
Go down through a hatch that Magnusson will open for you.
Then get to a lift and go down. Head towards the valve and turn it down.
Go straight ahead. You will get to a locked door. If Vort doesn't open it for you when you're there, just shoot at the window. He will notice you then.
Walk through the door he will show you and take the supplies on your way.
You will meet one of the rebels. Follow him. As soon as he walks through the door, the alarm will turn on. The door will close. Get to the stairs behind you. There is a passage to the left. Crawl in.
You will get to a warehouse full of hunters. Try to kill as many of them as possible (there will be 3 of them). Use the holes in the wall of the tunnel.
When you get rid of the hunters, go out of the tunnel.
Take any goods, then get on the upper level and head towards the left side of the room. There will be a valve. Turn it down and climb up the ladder.
Go straight ahead. You will get to a tunnel with flares. You will have to kill some Combine soldiers there. Be ready to destroy a turret which is at the end of the left corridor. When you do so, keep going the right corridor.
You will get to a flooded room. There will be some soldiers and a turret. You can destroy it using the gravity gun. You will just have to knock it down.
Go straight. You will get to a tunnel. Shoot the barrels when the soldiers show up. You will save some ammo.
You will get to a room with supplies. Grab them. Then you will get to a staircase. However, the stairs will be broken. Dive into the water under the stairs.
You will get to another room. Going straight ahead you will see a ladder.
Climb up. You will hear a music again. Combine soldiers will show up. You will have to close the silo. The silo is oval. On every level you will have to run around it to get to another ladder . Focus on running only, reduce the shooting to minimum. Climb up the ladders to get to the top.
When you're finally there. Walk across the footbridge.
Keep going. At the very top, you will have to deal with soldiers and flying drones.