There's a turret straight ahead. Don't bump into it. Instead, create a portal on the ceiling on the other side of the wall, then another on the wall in front of you where the next turret can't see. Pick up the nearby turret and drop it through the portal. If you're lucky, the turret that you dropped will shoot the next one, disabling both.
If you didn't disable the next turret, peek around the wall to shoot a portal behind it, then shoot a portal close to you. Go through the nearby portal and pick up the turret from behind, then make a portal on the ceiling and a portal on the wall, and drop the turret through, making sure you can take cover.
The floor beneath the third turret can take portals, so create a portal on a ceiling and then create a second portal under the third turret to disable it.
Go up some stairs and you'll see a cube. Just around the corner there is a fourth turret. Create a portal on the ceiling above that turret, then a portal of the other color beneath the cube. That should drop the cube onto the fourth turret, disabling it.
The fifth turret is behind some glass. Create a portal on the ceiling above it, then a portal below a cube to drop the cube onto the turret.
Next up is a large area with several turrets. There is one near the exit. Create a portal on the ceiling somewhere, then create a portal of the other color under that turret. Take cover and wait for it to be disabled.
If there are any remaining turrets, try to drop things on them or drop them through portals to disable them.
When they're all gone, drop a cube onto the big button and go through the particle field. The walkway is broken, so drop down. Go through some doors and you'll end up in the next test chamber.