- Edit the question with more information to clearly show that it's not a duplicate. You'll probably want to provide a link to the not-a-duplicate
- Leave a comment to the effect of "I've edited my question to show why it's not a duplicate of X"
- Vote to Re-Open
- (optional) flag for Moderator attention and use the "Other" option to explain that it's not a duplicate
Remember: "Closed" is not an end state; it just means that no new answers can be posted. In most cases, you have a couple of days to improve the question before people will (can) vote to delete it. It's expected that you'll use that time to improve the question.
If the above fails, you can also post a bounty on the duplicate question to try to get a better answer.