The old-fashioned way, of course! Here's an excerpt describing how people traveled to one of the the Lincoln-Douglass debates, this one held in Freeport, Illinois:

It was a cloudy, cool, and damp day. Special trains brought people from Galena, Chicago, Rockford, and other cities in northern Illinois. Estimates as high as 15,000 were reported in various newspaper accounts.

Lincoln answered the seven questions Douglas posed at Ottawa and then asked four of his own. Douglas' response became known as the Freeport Doctrine which had ramifications at the 1860 Democratic National Convention.

Source: Neely, Mark E. Jr. 1982. The Abraham Lincoln Encyclopedia. New York: Da Capo Press, Inc.

Those not present were left at the mercy of journalists, who were often shameless in promoting their favorite candidates and slandering opponents.