How exactly voting worked varied depending on time and place. Elections as we understand them in the US today largely date from Progressive reforms from the early 20th century onward.

Elections in colonial Virginia, for example, would be considered massively corrupt by our standards today. Voters gathered at the county courthouse, and votes were cast in-person, and by voice. There was no secrecy to your vote, so everyone, including the candidates and all of your neighbors, knew exactly who you voted for. These elections also featured fairly significant amounts of what we can with no great measure of injustice characterize as bribery. Even though the practice was strictly speaking prohibited, it was very common for candidates to provide voters with generous quantities of food and alcohol on election day. The idea that your vote was your own private business was foreign to colonial and early national America. Kentucky continued using a form of voice voting until 1891. For many American elections, voting was an open affair.

Even when paper ballots were used, it was not always a secret for which candidate or which party you had voted. Unlike today, there were next to no government rules governing ballot access. Virtually anybody with a printing press and enough paper could print ballots. Political parties and reform associations alike could print them. The parties, usually through their friendliest newspaper, sponsored the ballots themselves. In order to vote, you had to make sure you went to the Democratic or Whig or Republican booster at your polling station and get the right ballot for that party. Therefore, your vote wasn't even really secret. Parties sometimes printed ballots on specific colors of paper, so that could give things away too. If you wanted to split your ticket - vote for candidates of different parties - you would have to scratch out a name on the ballot and write one in.

With all of this in mind, there have been some fairly naked attempts at vote buying, some of it quite well documented. In the Gilded Age, some party organizations used vote buying shops. Here's how it worked: actually giving somebody money in exchange for a vote was a bad idea, but there was no rule against giving somebody, say, a token in exchange for putting in a ballot for the "correct" party. After you cast your ballot, you would go to the location of a vote buying shop, and sell your token for a certain amount of cash. We even have records of political fixers budgeting for how much money it would cost to buy votes in given areas - rural areas were generally more expensive.

As far as how long it took to get results back, it really depended on time, place, and the nature of the election. For local elections, same day results were in the cards. After the invention and widespread use of the telegraph, collecting returns statewide occurred much more quickly. Presidential elections used to be far more confusing than they are now because until 1848, not every state held its presidential elections on the same day. This, for reasons that should be obvious, slowed the process considerably.

So the thoroughly unsatisfying answer to the question of how secure American elections were is: it depends. A local election run entirely on voice voting could be said to be secure in a certain sense, but not fair by our standards. Both voice votes and votes by paper ballot were the objects at times tremendous social pressure to vote one way or the other. Cheating the system, were one sufficiently motivated, was not tremendously difficult, and the kinds of shenanigans that went on helped create the process we know today whereby the political parties function partly as means for controlling ballot access.

Readings

Joel Silbey, The American Political Nation: 1838 - 1893

Mark Wahlgren Summers, Party Games: Getting, Keeping, and Using Power in Gilded Age Politics

Charles Sydnor, Gentlemen Freeholders: Political Practices in Washington's Virginia

Richard Beeman, The Varieties of Political Experience in Eighteenth Century America