What was a popular form of entertainment for the Americans at home

If your question is referring to a popular form of entertainment for the Americans at home during World War II, then the correct answer is music from Swing bands, Radio, movies, and musical plays.

The Government of the United States considered important to maintain the moral of the citizens during World War II. For instance, the U. S. Office of War Information controlled the features of the movies in order to maintain the hight spirit of the people. U. S. citizens also liked going to the Dance Halls or Ballrooms in order to listen to music and dance with the music of famous orchestras like the Glenn Miller's orchestra.

Well I do not really know what time period you are talking about but, if you are talking about before TV I'd say doing things like listening to radio, playing games, and hanging out with others.