Basically, you request a mail-in ballot. You are checked to see if you're registered to vote. If you are, one is sent to you. You fill it in and mail it back by the required date.
You sign a declaration on that mail-in ballot. When the votes are counted, your details and your signature are physically checked. If they're accepted, your ballot is added to the pile, basically.
So your ballot isn't associated with your name but the envelope it came in is.
There are lots of checks on integrity for this sort of thing. Monitors from the major parties who can object to whether a signature matches that which is on file and so on.
The signature part is problematic. Many (most?) of us don’t have a need to use handwriting in our day-to-day lives. I rarely even need to endorse checks. And my official signature on either my license or SSN card are from years ago.
While my signature is fairly consistent with key parts looking similar, I almost never end up with duplicate looking signatures. An expert could probably identify them as being from the same person. A layman could almost certainly challenge the signature and win.
This happens. I was challenged in person on my signature by a layman despite having matching photo ID (drivers license). There's no training on how to frank signatures, not in Florida anyway. I won.
This does not address any of the issues that people complain about? How do you stop somebody other than the person who is supposed to vote from voting using the person's ballot and faking the signature? Or a person could sign the envelope and give their ballot and envelope to somebody else to vote.
The point of voting with an id is to look at the picture and compare with the person to confirm they are the actual person.
edit: before you say they check the signature. It is not reliable. I know people who have had to confirm their signature despite it looking close. I've scribbled my name not even close to what I had recorded and it worked fine.
I've lost over 150 pounds from the time I last had a photo id taken, mostly due to illness. I've grown facial hair to hide some of the lines in my face so that I don't look as sickly, and it is incredibly hard for me to get around. Should I be denied the right to vote because I don't look like the fat man in the picture?
The verification on retail transactions and on ballots have nothing in common. Signatures on ballots are validated by humans, usually with multiple observers who can object to any specific signature.
If you don't want voter id then having a national id is not important?