Owners of the Lumia 1520 can head into their Settings > Phone Update > Check for update to begin to receive the latest OS from Microsoft and new firmware to enable advanced features from Nokia.
AT&T did not comment on timelines for their other Lumia phones, though presumably they are not too far behind the Lumia 1520.
Our in house AT&T Lumia 1520 is not showing an update is live just yet, but our phone is running the Preview for Developers. It is not clear if we need to rollback the Preview in order to pull the update, though we will follow up shortly on that matter.
For more information about the Lumia Cyan update, please see our tracker page for all the latest.
Final Update: Microsoft is advising those with the Windows Phone 8.1 Preview enabled to downgrade the OS first before getting Cyan. More information can be found here.