Prior to the late 19th century (i.e., prior to William Jennings Bryan's populist Democratic campaign in 1896), it was rare for Presidential candidates to campaign for themselves in the way that we have come to expect, making personal appearances and speaking before crowds. That yeoman's work was left to proxies - representatives or allies of the candidate, who first would represent the candidate at the party convention (he would, invariably, not attend), and then would travel the speaking circuit, making appearances on his behalf. This was done for two reasons: first, as you mention, travel was difficult in the era before steam transportation. Candidates couldn't hope to visit even a sizable portion of the electorate in person. Second, it was considered improper for a Presidential candidate to "stoop" to the level of personally soliciting votes. It was beneath the office, and therefore ought to have been beneath men aspiring to the office. So personal campaigning of that sort was rare, though it was not unknown. (See, e.g., William Henry Harrison's "log cabin and hard cider campaign" in 1840.) An exception that proves the rule was Stephen Douglas's 1860 campaign, one of the few from this period in which the candidate campaigned personally. Douglas - a northern Democrat - crossed the country on a speaking tour, making a point of visiting communities in several hostile southern states. He knew that his own candidacy was a lost cause (his party had fractured in the run-up to the campaign, and it was increasingly clear to political observers that Lincoln was going to win the election with a purely sectional appeal to northern voters), and Douglas campaigned not for himself but on behalf of the Union, warning of the dangers of "sectional" politics, secession, and civil war.

Anyway, during a campaign, the Presidential candidate would typically remain at home. (Lincoln, for example, spent the 1860 campaign in Springfield, Illinois.) That is not to say that he wouldn't be involved in the campaigns, however. He would play a quiet, coordinating role, designating their representatives, making promises, crafting the campaign "message," and participating in certain artifices that allowed them to participate in the campaign without dirtying himself with common politicking. One such artifice was the use of letters written by the candidate and published in newspapers. Typically, these letters would be solicited by the candidate's own proxies, who would pose public questions to the candidate and invite the candidate to respond. (These were the 19th-century equivalent of "softballs.") The candidate would then be bound by politeness to respond in writing, providing some details about his personal beliefs or policy proposals. In this era, the press was almost purely partisan, with each paper having a stable party-political affiliation, so the letters would be published in the candidate's party's papers. This would likely be the only way in which the public would be "directly" exposed to the candidate prior to the election.

These campaigns were not, however, unrecognizably cold and distant from the people. Electioneering in the 19th century could at times be a much more populist, rollicking affair even than modern campaigns. Parties would hold rallies that were gigantic celebrations, ply potential voters with alcohol, and distribute mass-produced political paraphernalia that could be carried or worn by common supporters. Lincoln's campaign in 1860 formed young men into a mass organization called "the Wide Awakes," which held torch-lit parades and served as a kind of political police on his behalf. Some of the first nationally-recognizable advertising was for political candidates (e.g., "Tippecanoe and Tyler Too" in 1840), predating even the advent of mass media. Campaigns could also be exceptionally dirty - with proxies slandering (or telling inconvenient truths about) the other side's candidate. In 1800, the open secret of Thomas Jefferson's sexual relationship with his slave Sally Hemings was discussed and mocked in newspapers. In 1828, Andrew Jackson's wife was - correctly - accused of bigamy by his political opponents. Early (small-r) republicans were often tarred as revolutionaries, anarchists, and demagogues; Federalists were portrayed as monarchists and petty tyrants. When mid-century Democrats warned about the dangers of "black Republicanism," they were not merely using the color metaphorically, but were in fact accusing Republicans of advocating the mixing of the races (a phenomenon variously called "amalgamation" or "miscegenation"). So when the George W. Bush campaign in 2000 spread false rumors in South Carolina about John McCain "father[ing] an illegitimate black child," Bush wasn't doing anything that American politicians hadn't done for two centuries prior.