What would happen if two candidates tied in a states popular vote or if there was a dispute to the winner?

A tie in a popular vote can be handled several different ways depending on which state you're in. If the candidates who tied are not the frontrunner, it has no impact on the result of the election. The top vote getter still wins the election.

But, if the top two vote-getters tie, then it usually triggers a recount of the votes. Often, elections people have to recount every vote by hand to verify them. It is handled by highly trained teams of people with plenty of experience and overseen very carefully. If there is a winner by even 1 vote, the person with the extra vote wins.

If the result is still a tie after the second counting of the votes, a new election is held, but only with the two candidates who tied. If they continue to be tied, another hand count of the votes would be conducted to make sure that the votes are correct.

If they remain tied, not all states have the same requirements for what to do after this; but in some jurisidictions, the outcome can be determined by having the candidates each turn up turning up a card, calling heads or tails in a coin flip, or even picking straws. Whoever wins the contest wins the election. Those little games of chance are highly supervised so that there is no advantage for either candidate.

One little town out in the southwest got its name from a card draw game that actually did determine the outcome between two tied candidates. The low card won.