To create and distribute an Ad Hoc distribution build, first switch to the iOS Device destination in the Scheme pop-up menu in the project window toolbar. Until you do this, the Product → Archive menu item will be disabled. You do not have to have a device connected; you are not building to run on a particular device, but to save an archive.
Apple’s docs say that an Ad Hoc distribution build should include an icon that will appear in iTunes, but my experience is that this step is optional. If you want to include this icon, it should be a PNG or JPEG file, 512×512 pixels in size, and its name should be iTunesArtwork, with no file extension. Make sure the icon is included in the build, being present in the Copy Bundle Resources build phase.
Now choose Product → Archive. The build is created and copied into a date folder within ~/Library/Developer/Xcode/Archives; it also appears in the Organizer window in the Archives tab. Locate the archive in the Organizer window. You can add a comment here; you can also change the archive’s name (this won’t affect the name of the app).
Select the archive and press the Share button at the upper right of the window. A dialog appears. Here, you are to specify a Contents type; choose iOS App Store Package (the default). You must also choose an Identity; specify the identity associated with the Ad Hoc distribution profile for this app. (This is the step in which it matters which of the app’s distribution profiles you specify.) Click ...