The Republicans ran New York Governor and crime-busting prosecutor Thomas Dewey, the man who had successfully prosecuted mobster Lucky Luciano. In the campaign's final days many newspapers, magazines, and political pundits were so confident of Dewey's impending victory that they wrote articles to be printed the morning after the election speculating about the new "Dewey Presidency". Life magazine printed a large photo in its final edition before the election; entitled "Our Next President Rides by Ferryboat over San Francisco Bay", the photo showed Dewey and his staff riding across the city's harbor. Several well-known and influential newspaper columnists, such as Drew Pearson and Joseph Alsop, wrote columns to be printed the morning after the election speculating about Dewey's possible choices for his cabinet. Alistair Cooke, a distinguished English writer wrote an article on the day of the election entitled "Harry S. Truman: A Study of a Failure." As Truman made his way to his hometown of Independence, Missouri to await the election returns, not a single reporter traveling on his campaign train thought that he would win. The head of the Secret Service even left Truman's detail to be with Dewey, who he believed would be the next President. Truman went to bed in a Missouri hotel not knowing what the election of the outcome would be.
The Chicago Tribune, a pro-Republican newspaper, was so sure of Dewey's victory it printed “Dewey Defeats Truman” on election night as its headline for the following day. A famous photograph taken the next morning showed Truman grinning and holding up a copy of the newspaper. The key states in the 1948 election were Ohio, California, and Illinois. Truman narrowly won all three states by a margin of less than 1%. These three states had a combined total of 78 electoral votes.
The final result in the Electoral College was 303 for Truman, 189 for Dewey and 39 for Thurmond. I found a great YouTube video from the PBS documentary on the life of Truman. Unfortunately, embedding is disabled, but if you'd like it see it, it's 3:12 in length and contains Dewey's very gentlemanly concession speech. The video can be found here.