Dumb Question: Voter Identity in USA, Easy to Cheat?

As you may know, I've never voted in American Elections. We made aliyah a couple of months before my first possibility. In those days, voting age was twenty-one 21. I turned the age in May, got on the boat late August, and Elections were in November. It never even crossed my mind to apply for an Absentee Ballot. And over the almost half a century since then, I've gotten no further than mulling over the issue.

Here in Israel voting is very organized and it's pretty hard to cheat, other than those who arrive with an Identity Card of a similar looking dead person who hasn't been registered as dead, or the same sort of thing with someone hospitalized. As long as nobody in the polling station staff realizes it or "squeals," it can be done.

wikimedia.org

Yes, in Israel we have Identity Cards, with pictures. Some of us have very old ones, which can be problematic, since we don't look much like the photos. That's why there's usually a lot of pressure on the staff in the Ministry of the Interior to produce new cards for many in the weeks before an election. 

In Shiloh and other small communities, there's pretty much always a neighbor on the "staff" who can easily vouch. Also, we're all sent notices telling us exactly where we are supposed to vote. And we must vote there. If there was a mistake by the clerk in the Ministry of Interior, which happens --such as sending someone to Shilat, rather than Shiloh-- one can get free public transportation.

There's no "absentee ballot/voting" in Israel. The closest is the voting by soldiers, diplomats stationed abroad, etc. And those ballots are in multiple envelopes to preserve secrecy. On the outer envelope is the name and ID number of the voter. After polling station votes are counted, then those envelopes are checked to see if that ID number had voted in person. If so, the envelope is voided, ripped, destroyed whatever.

Now, in the United States, there aren't required Identity Cards, and from what I've read, there is no longer an assigned place to vote. So how does it work? Besides just trusting people...