According to the webpage, you only need a WiFi connection once to activate the authenticator application, and after that you're all set.
This comes right after the transition of the EU World of Warcraft account management to the new Battle.net account management. The US transition is reportedly done, although there has been no official world from Blizzard yet (however all their webpages have already changed over).
The app is not available for download yet via Blizzard or from the Apple store. But we'll let you know the second it goes up!
You can read the full FAQ after the break, or check out the Blizzard Support article.
Where do I get a Battle.net Mobile Authenticator?
The Battle.net Mobile Authenticator application can be found at this link depending on your mobile phone model and/or mobile service provider.
What is an Authenticator code and where do I see it?
The Authenticator code is an eight-digit numeric code that is produced when you select "View Code" in your Battle.net Mobile application. Each code is unique and is valid only once.
Do I need to have an active cell phone signal or access to a wireless network in order to use the Battle.net Mobile Authenticator? Why is airtime required for use?
Airtime is only required in order to enable your Battle.net Mobile Authenticator for the first time, or in the rare case when you may need to re-sync or reset the Authenticator. Once you have enabled the Authenticator, you do not need to be in range of an active cell phone signal or have access to wireless service in order to retrieve a code to log in.
Will this application work with an iPod touch?
Yes. However, you will need to have a valid Wi-Fi connection in order to enable the Battle.net Mobile Authenticator for the first time, or in the rare case when you need to re-sync or reset the Authenticator. Once the Authenticator is enabled, you do not need to have a network connection to generate a code to log in.
Can I use a Battle.net Mobile Authenticator and a Blizzard Authenticator at the same time?
You can only have one Authenticator attached to a Battle.net account at any given time.
How do I remove the Battle.net Mobile Authenticator?
You can remove the Mobile Authenticator through Battle.net Account Management. Please do not simply delete the application without first removing the Battle.net Mobile Authenticator from the associated account.
What happens if I lose my mobile phone after activating the Battle.net Mobile Authenticator?
Please contact Blizzard Customer Support if your phone is ever lost or stolen so that we can take appropriate action.
What happens if I delete my Battle.net Mobile Authenticator application from my mobile phone? Can I still log in to the associated account?
Unless you remove your Battle.net Mobile Authenticator from the account prior to deleting or overwriting the Battle.net Mobile Authenticator application, you will not be able to log in to the account. If you remove the Battle.net Mobile Authenticator application prior to removing it from the account, please contact Blizzard's Billing and Account Services team. Our representatives will be able to assist you with regaining account access by verifying certain secure information with you.
Will a Blizzard representative ever ask for my Battle.net Mobile Authenticator information?
Yes. Blizzard may ask for the serial number associated with your Battle.net Mobile Authenticator, typically to help you associate it to an account or to verify your ownership of that product.
Can I apply my Battle.net Mobile Authenticator to more than one account?
Yes! You're welcome to associate a single Battle.net Mobile Authenticator to as many accounts as you like. Please remember that you must have the mobile phone with the Battle.net Mobile Authenticator with you to log in to any of these accounts afterwards.
Please keep in mind that a single Authenticator will provide secure access to all of the World of Warcraft accounts associated with an individual Battle.net account.
Many thanks to Tlann for the tip!
Updated 5:05 p.m. EDT: Changed the note about the U.S. transition to Battle.net accounts.