^ I'm beginning to doubt you've ever voted before.
You register to vote. Based on your address, you are assigned a precinct. When it is time to vote, you go to your precinct, give them your name and voter registration card, and they look at the registration logs. If you're on the logs, they check your name off, you go into the booth and vote. If you're not, you cannot cast a regular ballot. There is no way for one person to vote twice/thrice.
As for the voter ID suppression Republicans are running, I urge you to watch John Oliver's show from this evening (ironically enough, I had no idea he was going to do a piece on this issue tonight and I left my computer to go watch it right after I responded to you). If you don't have HBO, I'll link the piece when it is available. I hope you watch it and form your own opinion. It is blatant voter suppression, performed and supported by only one party, without any evidence of fixing non-existent "voter fraud", and open admissions that the purpose of requiring voter ID is to win elections for Republicans.