If I was a civilian back home and had a big interest in the war, what would I be doing to keep tabs? Anything beyond the daily newspapers?
Newspapers.
Real time news had been a thing for decades prior to the World War I, especially in the financial industry. The printing telegraph enabled unskilled workers to transmit and receive text. This photo from 1918 shows employees at the Waldorf Astoria hotel in New York transcribing from a stock ticker. Newspapers relied heavily on agencies like Reuters or Associated Press, but anyone could become a subscriber if they had the money.
Edit: There are some nice photos and technical details of period teletype equipment here, including this photo of a 1905-vintage Murray setup.