Here's how it works. When you sign up, you'll be asked to make a toll-free call from a specific phone of your choosing to authorize login attempts with the battle.net account. You get to assign the phone number that is used, and if there is something unusual about the login attempt on your account, you'll be asked to call the toll-free number to verify you are you. An example of unusual activity would be playing from a different location than you normally do. In other words, if a keylogger gets hold of your account information and attempts to log in, they'll be prompted to call the number -- and they won't be able to go any further, because they don't have your phone and they don't have your PIN. You will only be asked to call if it's an unusual login -- otherwise, you can continue to log in and play with no worries.
The Dial-in Authenticator is currently only open to U.S. residents, and it only covers World of Warcraft accounts -- although Blizzard may update it to cover more countries in the future, as well as StarCraft 2 accounts. In order to sign up for the Dial-in Authenticator, you must log into your account on Battle.net, then go to Security Options and choose to add the Dial-in Authenticator. If you already have an authenticator on your account, you must remove it in order to sign up for the dial-in service; you cannot use more than one security method at a time.
For more information on the service, check out the official FAQ on Blizzard's website.