How does it work? I am on OS X 10.8 Mountain Lion.
There is one big caveat: the developer must have made the last compatible version available.
Then: http://support.apple.com/kb/ht5919
If I go to the purchased tab in the App Store, and click on download for a given application, I get a popup which states "Download an older version of this app? The current version requires OS X 10.9 or later, but you can download the last compatible version."
I don't know if it works for apps you have not yet purchased.