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  1.  
    The Organizer badge is awarded for the first retag, but you need 500 reputation points before you can retag questions. Having said that, when I click on the Organizer badge, there are lots of people who have been awarded this badge with less than 500 reputation points. I must be misinterpreting when the badge is awarded. So my question is the one in the title: How is the Organizer badge awarded?
  2.  
    I think the 500 rep limit is only for retagging the questions of others. They have probly retagged their own questions.
  3.  
    How do you retag your own question?
  4.  
    Right under the tags of your question, you can read "edit". Clicking there allows you to edit your post, which includes changing tags.
  5.  
    I have previously added tags and deleted tags on questions that I have asked, but I haven't been awarded the badge. I'm not complaining, I just don't understand how it works.
  6.  
    I think I have the answer. I have an organizer badge and yet my reputation is less than 500. I did it by adding a tag to a question (not mine) that was community wiki.
  7.  
    Just for the record: I recently asked a question on MO. Shortly after I deleted one tag and added another, but I still wasn't awarded the Organizer badge.