I have been an election judge, and the process is quite simple.
The voter presents himself and his ID, usually a Drivers License, and the election judge asks him what his address is and normally it is the address printed on the ID. Then he is handed a ballot and shown to a booth where he votes by marking an X on the ballot. When he is finished, he signs the ballot, hands it to a judge who checks to see that it is signed and then gives it back to the voter who places it in a slot. Then he gets an "I VOTED" sticker and leaves.
There is almost no opportunity for the ballot to be illegal or the voter to be someone other than the person on the driver's license.
In 2020, I received a ballot by mail, and I deposited it in a box supervised by an election judge, who checked my ID.