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I'm running Lion, how do I do this? I don't use the mail app, by the way?

To sync notes through iCloud you have to have a MobileMe account (@me.com email), but even before iCloud all notes are synced through Apple Mail. As far as I know, the only way to do it is through the Apple Mail on your computer.
 
If you have iCloud set up just go into mail, and click the new note button. It will sync immediately to all your iCloud devices.
 
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