When planes land, do they receive a hardline connection to ATC in order to receive the next flight plan, or do they receive their flight planes wirelessly from ATC?
The airline files the flight plan to the air traffic control (ATC) on behalf of the crew. The crew receive the print out before the flight.
The airplane "receiving" the flight plan can then mean one of two things:
Flight plan programming
The crew will use this printed flight plan to setup/program the FMS in the cockpit.
Alternatively, the airline can send the flight plan to the crew wirelessly via ACARS, the crew then prints it out in the cockpit.
If the route flown is frequent and rarely changes, the airline can have it saved on the plane, the crew will then load the saved plan, and revise it—making sure it matches the print out.
It's time to get on with the flight
The crew will call ATC on radio requesting clearance to their destination as filed.
If everything matches, they get the go-ahead. If not, amendments will be relayed, and changed accordingly in the FMS.
Any digital communication is subject to airport, airline, and airplane equipment.