I'm downloading Mavericks on my Lion, but I don't know how to see the progress. When I go to the purchases tab on the app store, I see a blank button:
Quit App Store, open Launchpad, find the partial download of Mavericks installer and click it. This usually resumes a download that was interrupted/paused.
Reset App Store by clicking Reset Application from the debug menu, then reboot and try again.
You can enable the debug menu by running the following command:
defaults write com.apple.appstore ShowDebugMenu -bool true
It turned out, that it was a 'hidden' purchase, and I had to go to my account and unhide it.
Thanks to this answer.