How can I get a ride in the jump seat as a non-professional pilot?
It's hugely unlikely. Almost vanishingly unlikely, with few exceptions perhaps for something a little smaller than a passenger-carrying A380 (like a private jet on a repositioning flight where you know the captain well)

You used to be able to go up and see the captain on the flight deck - I did it a few times as a kid. Even then asking to sit in the jump seat was usually met with a smirk. 

And then 9-11 happened.


  With effect from 1 November 2003, ICAO Annex 6 was amended so that under Chapter 13.2.2 “all passenger-carrying aeroplanes of a maximum certificated take-off mass in excess of 45 500 kg or with a passenger seating capacity greater than 60 shall be equipped with an approved flight crew compartment door that is designed to resist penetration by small arms fire and grenade shrapnel, and to resist forcible intrusions by unauthorised persons. This door shall be capable of being locked and unlocked from either pilot’s station”.


And with that came locking of the cockpit door, and no more visits to the cockpit during flight (incidentally, if you ask nicely, the captain will often let kids take a peek when they're deplaning the passengers)

And then germanwings happened, and they had a rethink. But still no visits to the cockpit during flight at all for the average Joe.