Jump on the faith plate until the ceiling is lowered. Place portals so the faith plate shoots you up through them to the upper level. Put one portal on the ramp that goes to the button and use the faith plate to press it. Do the same on the other ramp to get the cube that just dropped.
Redirect the laser like in the picture, then use the third ramp to faith plate yourself up to the exit platform. From here place you portals on the wall you redirected it too so it goes into the receiver on the other side.
Take the faith plate up one floor, then setup your portals to fling yourself over to the cube. Grab it and take it up to the first laser, and block it. Jump down and take the faith plate again to go up two levels.
Press the button and catch the laser cube. Take it down one floor to the first laser. remove the cube and replace it with the redirection cube so it faces the white wall in the picture. Place a portal there, grab the normal cube and take the faith plate. Place the other portal on the wall so the laser goes into the receiver. Grab the cube, and take the faith plate one last time. Place the cube on the button.
New element, the light bridges! Portal across to the other side where the button is, and notice how the bridge goes through the portal. The button activated the cube dropper.
Stand in the middle of the bridge over the gap, and change the bridge to where the picture shows. Follow the path and keep doing this trick to get to the cube. Grab it and head through your portal back to the start. Then just use the bridge to get to the exit.
Use portals to get the bridge, go back to the start with it, and line it up underneath the cube dropper. Press the button, catch the cube and use the bridge to take it to the exit door.
Turret time! Don't stand in front of them for too long, or they'll shoot you silly. Pick up and drop the first turret from behind. Peep around the corner and shoot a portal behind the second turret to get behind it. For the third turret, just quickly put a portal underneath it, it'll fall over by itself.
Next part involves using portals to drop objects on top of turrets to knock them over. Do this for the two in the hallway and progress onto the three by the exit door. If you're out of cubes to drop, using dead turrets also works.
Next room is easy, use the cube and portals to redirect the laser through all the nodes.
Note how the turrets can't see you through the light bridges. Portal the bridge so you can get past the first turret. Place the bridge as a wall on your right side so you can pass to the back of the room.
Place the bridge where it is in the picture and jump on a faith plate to land on the roof. From there, walk across the glass and drop down behind the 4 turrets. Knock them all over and take the cube. Before placing it on the button, put the bridge so the two turrets by the exit can't see you. Then, portal behind them and take the exit.
Stand on the button and use portals to line the laser up with the three turrets to blow them up. Go and grab the two cubes, putting the normal one on the button. Take the redirection one to the end of the laser, and redirect the laser through the glass to blow up the other turrets. Then, redirect it into the receiver and go to the exit.
Extend the bridge over the button, and move the cube overtop the button so it also blocks the laser. Stand on the moving platform and change your portals so the bridge disappears and the cube falls on the button. The laser will also go into the receiver, the door will open and the moving platform will rise.