It's kind of a pain in the ass. I don't even do it every year. You have to take your DD-214 to the county recorder or something like that, and they they do something with it there. I can't remember because I didn't bother trying to figure out how to do it again this year.
They don't mark your license at all to show veteran status. It's just a declaration to the DMV. I don't even know if they require proof for this "declaration."