How do I export an XCode app so I can publish it on my website, not in the Mac App Store?
You have to export you application as a .app bundle and then it's the .app bundle that you sell or give away on your own web site to pass the application along. From this SO question:

In XCode 4, applications are exported from the "Organizer" and you build a .app bundle for redistribution by building an archive of the application:


On the menu go to Product -> Archive
Once you're in the Organizer - Archives screen click Distribute button if you're using XCode 4.3.3 or higher, click the Share button for releases before 4.3.3
Then choose the format you want to export.