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.