Primarily through word of mouth, and secondarily through pamphlets and newspapers (because at least in Jacksonian times, most of the public still could not read or could with great difficulty). When famous French political theorist and writer De Tocqueville visited America in the 1830s, he noted a highly civically engaged society and high degree of free association and intermingling of various classes (most true in the Antebellum Era) in public society where people often shared their ideas, discussed politics, and where political candidates canvassed for votes.

As De Tocqueville writes:

Americans of all ages, all conditions, all minds constantly unite. Not only do they have commercial and industrial associations in which all take part, but they also have a thousand other kinds: religious, moral, grave, futile, very general and very particular, immense and very small; Americans use associations to give fêtes, to found seminaries, to build inns, to raise churches, to distribute books, to send missionaries to the antipodes; in this manner they create hospitals, prisons, schools. Finally, if it is a question of bringing to light a truth or developing a sentiment with the support of a great example, they associate.

source: Democracy in America. Alexis de Tocqueville