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When Mountain Lion officially launches in the Mac App Store, simply visit Apple's Up-To-Date page. Fill out a short form with basic contact information and the serial number of your new Mac. Once the information is verified, Apple will email you a redemption code to claim a copy of Mountain Lion in the Mac App Store.
The new version of OS X is expected to be released following Apple's Q3 earnings call scheduled for July 24. You will have 30 days from the release date to take advantage of this free upgrade.