After you have purchased the official copy of OS X 10.8, the Mac App Store will take you to Launchpad, but the download will not begin instantly. You will be “waiting” for OS X 10.8 to download.
Go back to the Mac App Store, hit Purchased and click on “Download.” The moment you click the “Download” button, your Mountain Lion installer should begin downloading.
Sometimes the download button can be grayed out. If that’s the case, relaunch Mac App Store and try to download again.