I would quibble that "democratic" is perhaps an inapt term. For example, I personally use "democracy" today to mean sovereignty exercised by universal adult suffrage (modulo a few who are disqualified, and usually limited to citizens or the like). Under that definition, there were no "democracies" before the 20th century. Indeed, "democracy" was something of a term of abuse in the US just after the Revolution.

Voting in Early America touches on, well, Voting in Early America.

Sheriffs posted notices of elections in prominent places throughout their bailiwicks. On the appointed day, voters traveled to a courthouse to cast their ballots. ... Diversions aside, the main election-day business was to vote. A few colonies, including Pennsylvania, Delaware, and North Carolina, employed some form of ballot. Others, like Virginia, relied on public voice votes, an English tradition. Voice voting made ballot counts harder to rig and, cast in the presence of friends, neighbors, local officials, and candidates, left no doubt about a voter's intention. In Virginia, voice voting was a spectator event, every voter occupying center stage for a few moments. In his book Gentlemen Freeholders: Political Practices in Washington's Virginia, Charles S. Sydnor wrote:

As each freeholder came before the sheriff, his name was called out in a loud voice, and the sheriff inquired how he would vote. The freeholder replied by giving the name of his preference. The appropriate clerk then wrote down the voter's name, the sheriff announced it as enrolled, and often the candidate for whom he had voted arose, bowed, and publicly thanked him.

Apparently, voter turnout usually was low. Voting, especially in rural areas, took effort. Voters might have to travel a long distance to a courthouse and sometimes paid for food and lodging.

Recall that at the time there were stiff property requirements or tax requirements in many (most? almost all?) places in colonial America. I expect that anyone in a county who had "fifty acres of land or property worth 40 [pounds]", for example, would be well known.

Yes, public voting. "Australian ballot" sometimes today refers to a scheme of proportional representation, but originally it meant "the system of voting in which voters mark their choices in privacy on uniform ballots printed and distributed by the government or designate their choices by some other secret means", from 1856 in Australia, "In Great Britain the secret ballot was finally introduced for all parliamentary and municipal elections by the Ballot Act of 1872. In the United States, the Australian ballot system was extensively adopted after the presidential election of 1884." The EB on Australian ballot.

By the way, I believe a secret ballot was somewhat controversial, though I don't have a source. One argument for public voting was that it was disreputable for a man's vote to be secret. So "vote fraud" could go the other way, particularly notoriously in the UK. There were some electorates that had few electors. If there was a powerful man there, and if electors tended to be his tenants or otherwise dependent, he would make his will known and verify that everyone followed it, and punish those who did not. The term is "rotten borough".

As for knowing the candidates, the article notes

Before the Revolution, colonists generally did not vote for their governors ... Many colonists did not choose their local officials. Some governors, like Virginia's, appointed justices of the peace, sheriffs, coroners, and clerks. Some towns in such colonies as New Jersey and Pennsylvania, however, had local elections.

For US senators: until the early 20th Century, senators were elected by the legislatures of the various states (though some states had instituted forms of referenda as a rules hack to attempt to allow the people to elect senators).