How is the Flight Plan Data transferred into an aircraft/plane?
First, as other answers have stated, you're not actually required to file a flight plan unless you're flying IFR. That having been said, if you do file a flight plan, there are several ways you can get it programmed into the airplane:

You don't

The flight plan is never loaded into the navigation system at all. It's either on paper or loaded into a tablet, and that's it. This is pretty common amongst small-aircraft private pilots.

Manually

The flight plan is printed or loaded into a tablet to get it out to the airplane, where it's then manually keyed in to the on-board navigation system. This was at one time the only way of loading a flight plan, and is still pretty common across all types of aviation.

Bluetooth

This is a pretty new option for the higher-end GA aircraft and charter aircraft. The flight plan is transferred from a tablet, laptop, or smartphone to the onboard navigation system via a Bluetooth connection.

ACARS or other data link

Yes, ACARS is used by the big airlines to transfer flight plans to aircraft. Note, however, that some commercial aircraft don't have the capability to automatically transfer the flight plan to the navigation system(s), it's printed out by the in-cockpit printer and keyed in to the navigation system as described above.