The process is simple and a little complicated at the same time. Remember the United States is a republic, not a democracy.

Sure, we vote for a person on the federal presidential ballot, but only indirectly as we are actually selecting electors to vote in our place.  That’s the procedure outlined in the Electoral College.

For state elections most states utilize a popular vote to determine who wins. Some states, or jurisdictions within a state, may have enacted instant runoff voting (IRV) rules where even if a candidate wins the popular vote another candidate could win with fewer first place votes but with more second and third place votes overall.

Sometimes the vote is so close provisional ballots are counted to get a more accurate final tally. And sometimes, when the vote is extremely close, election committees can decide to take a look at the ballots cast to determine if they are valid or were misinterpreted.

For an interesting and in depth study of the American election process go to https://www.usa.gov/voting-laws-history