Start from rally point Alpha and drive towards the cliffside area, ignore the enemies and carry on towards the river where you fight some enemies, some marines should be there.

Grab a plasma pistol and look around to see the Falcon, it should be flying in a triangular pattern, work out where the Falcon goes and where to fire the EMP blasts off the plasma pistol.
If you EMP it, it will fall straight down, but keep EMP'ing it else it will just fly off again. in order to pilot the Falcon, it must be EMP'd and flipped upside down so the pilot comes out, if not you can always get in the passenger seat, but getting out means you will fall to your death.

However, if Carter and the marines kill the rest of the enemies then the Falcon will drive off towards Kat and Emile and Jorge and Carter will just appear in their seats. If you are in either of their seats you will be merged together and you can take a pretty cool screenshot of you and carter merged.

Once you start piloting the Falcon there is no way of getting out except by getting hijacked by an elite, if every elite at the river is dead, go to where Jun points out heat signatures in a building, there should be only 1 elite so don't kill him.

Once the elite hijacks you he will immediately get out without his weapon in his hands, so he will pretty much just push you around and not even melee you.

If you have Jorge, Carter and/or Jun are in the passenger seat of the Falcon, they will not get out unless flipped over, if there is no one piloting the Falcon carter may start to pilot it and immediately start flying off, but all he will do is crash into the side of a mountain.

You cannot fly to where Kat and Emile are so if you wish to continue onwards then you must get the original pilot to start flying the Falcon.

I am not sure wether this cheat works in campaign matchmaking, but when I tryed EMP'ing the Falcon of the cliffside area down, it didn't fall after it was hit by the EMP.

If you try to do this cheat on the Falcon around the cliffside area when you're not in campaign matchmaking, then the Falcon should fall unlike it did in matchmaking.