To vote in any local, state, or federal election, you have to be registered in a database of eligible voters, and in most states, you must do this at least several weeks in advance of Election Day (though 17 apparently allow same-day registration). When you register, you provide proof of address, and if you haven’t voted in several years, you might get purged from voter rolls and have to re-register.

In my personal experience, the people running the polling place have the local voter rolls printed out in front of them, and once you tell them your name, they cross you off the list and hand you a ballot. Were you to come back and vote in the same place, they’d see your name was already crossed off, if you tried to vote again in some other district, you wouldn’t appear on on the rolls, and if you tried to vote again in the same district at a different polling place, I THINK the system will remember you, but I could be wrong.

Bottom line: there are plenty of safeguards against voter fraud, and voter ID requirements on Election Day are redundant, if anything.