Radio, but mostly newspaper was the source for news including baseball.

In the midwest, the Cardinals had radio affiliates throughout the plains states and some still exist today that go back to the 1920s. Also many places you could pick up the strong AM stations such as WGN out of Chicago for long distances (to Denver and Dallas!).

There were also many minor leagues and teams, throughout the US, and those that were affiliated with major league teams, like now days would tie local fans to big league club..as they followed the careers of the guys they saw play locally.

Newspapers brought you the news and the box scores. The papers were usually delivered in the evening and had the box scores from either the prior day, or in some instances from two days prior. (the ability to read a box score is a dying art). Most middle class Americans took the daily newspaper, as it was their main source of news and editorial opinions on events.

The "Sporting News" was a widely distributed weekly newspaper and had write ups of baseball, all the week's box scores and was even called "the Bible of Baseball" by Roy Blunt in 1986 on the Sporting News 100 anniversary). It was a must have subscription for many baseball fans.

Also weekly "New Reels" were a Short film, that played before motion pictures at theaters, where you would see the news of the week and would sometimes include a brief sports clip of the major events of the week, and in the summer that of course was baseball.

In the post war 40's and into the 1950's on the west coast, many people followed the Pacific Coast league like a 3rd big league. Many players even refused to be called up to the "big leagues", and were paid almost as much as they would get in the major leagues. Until the Dodgers and Giants moved to California that is.