I posted it a while ago in another topic, but I thought that it deserves its own.
Only thing you need is your computer and a bit of computer knowledge (especially working with cmd).
Firstly, download Android SDK from Android's homepage, then update with chosen packages and corresponding APIs (doesn't matter which, it could be any version, even 1.5).
Then set up your AVD, you'll do this using Android AVD Manager, or through command line using android.bat and "create avd" command. First method is much easier, second is much more advanced. However, you don't need any advanced settings to use authenticator.
After you do this, run your AVD using AVD Manager (you can also make standalone shortcut on your Desktop: "location\android-sdk-windows\tools\emulator.exe" @youravdname) and download Battle.net Mobile Authenticator application package from here.
Then you must use command line, locate your "tools" folder in sdk location, it will look like this:
and type: "adb install [your bnet apk location, for example: C:\Bnet Mobile Auth.apk]" (if it displays an error "daemon is not running" then simply repeat the operation)
Now the last thing to do is to switch to your running emulator and run the application, after registering it on battle.net account management you can use it normally like on every phone, just run the emulator from avd manager or execute custom shortcut (method described above). There is also disadvantage, because emulator starts rather slowly, and WoW isn't running very smooth with Android in the background, but hey, it's free!
hope you will enjoy it.