Here's the story of basically every time I've gone to vote here in Texas.
When I arrive at the polling station, I present my voter registration card to the registrar. The registrar looks at the registration card, and usually asks me a couple of questions off the registration card -- my address, perhaps my date of birth.
I then am presented with a printout sheet with my name, address, and voter registration number. I sign this sheet. Then I vote.
So what's different if I'm required to show a photo ID?
In the Republican hypothetical where I'm attempting to vote as someone else (presumably a dead person), first of all, I would have to physically have their voter registration card in my possession. (If I don't, I'm already required to show photo ID -- but as long as you have your registration card, you don't.) Remember, the voter registration card already has all my information on it. If I, say, can't remember the address on my card or my date of birth or whatever question they ask me, bam. Voter fraud stopped.
Heck, if my voter registration card says I was born in 1923, the registrar would probably notice that I appear to be nowhere close to 90 years old.
And after all that, if I've managed to fool the registrar and everybody at the polling station into thinking that I am actually the person who is fraudulently attempting to vote -- well, I'd better be damn good at forging their signature, because the county elections office has the signature on file, and they can compare the two after the fact to see if they match. And if they don't? My vote doesn't count.
The best argument against the Republicans' insistence that everyone should have to show a photo ID in order to vote? You don't even need a photo ID to stop the mythical "voter fraud" that they so badly want to stop.