Nowadays when you cast your vote, generally the ballot has both the name of the candidate and (in fine print) a slate of electors pledged to vote for that candidate. Was it the same case in the 1788-89 election, or did voters choose electors without necessarily knowing which candidate the electors would vote for?
The first presidential election (1788-89) was more to decide whether or not the Constitution would be ratified than to elect an actual Leader. That should be said before I go on.
Anyway, if you look at the U.S. at that time, the methods varied. Places like Maryland and Pennsylvania had voters voting for Electors, while Delaware had a series of electoral districts that had voters voting for Electors. Meanwhile, Massachusetts, Connecticut, Georgia, New Jersey, New York, and South Carolina had their electors chosen (more or less) by state legislature.
Source is Founding the American Presidency. I wouldn't suggest reading it unless you've got the stomach for awkward word choice and purple prose in historical writing.