Well, the current demand for constant entertainment was not so popular during the early days of flight, and generally books or newspapers were considered suitable, especially given the short duration of many early commercial flights. Flying was still new enough that people looked out the windows (or in some aircraft such as the giant Russian commercial ones-- Grand and Ilya Mourometz) walked around in the open air on a walkway outside the fuselage. "This Was Air Travel", by Henry Palmer, Superior Publishing Co., Seattle 1960 discusses many of the problems faced by early commercial passengers, and lack of entertainment was not one of them.

Comfort, however, was an early competitive edge, and the larger aircraft of the 1920s offered kitchens, bars, decorations, and comfortable chairs. Maps for passenger use were provided early on, e.g. on the Handley Page W-10.

There were many competing problems, which really precluded much in the way of entertainment. Palmer notes that "Sound insulation did not exist. Neither did mufflers." In various early passenger craft, passengers could communicate only by written notes. On the Handley Pages, the Goliaths, and on the early Fokkers, passengers could make themselves understood only by screaming, and then only if the windows were closed. Vibration, Ventilation, and Cold caused more people problems than any lack of entertainment.

The development of larger aircraft, such as the S-23 Empire flying boats, allowed more use of stand-up bars, promenades, and meal service.

Now, on to your specific question--

The first in-flight movie was shown during Chicago’s Pageant of Progress in August 1921 on Aeromarine Airways showing a film called “Howdy Chicago” to its passengers as the airplane flew around Chicago. This was actually an advertising film for the city of Chicago, and other than its novelty seems to have been forgotten.The film “The Lost World” was shown to passengers of an Imperial Airways flight in April 1925 between London and Paris.

By 1929, Transcontinental Air Transport (TAT) had equipped its airplanes with movie projectors and screens, writes Daniel L. Rust in Flying Across America: The Airline Passenger Experience. In addition to comedies, advertising films promoting TAT services were shown.

In 1936, the airship Hindenburg offered passengers a piano, lounge, dining room, smoking room, and bar during the 2 1/2 day flight between Europe and America, but no movies.

I have no personal knowledge as to how the airlines pay for movies today, but they do buy rights from the movie companies.