You need a smartphone that runs at least Android 2.2 Froyo. Besides the initial authenticator (for key chain), Blizzard has also developed an authenticator app that runs on Android and iOS. We will talk about the Android app here but I guess the iOS one works pretty much the same.
Step 1: Download the app from Google Play, here.
Step 2: Install the app.
Step 3: Go to eu.battle.net or us.battle.net and login. “Manage my games”, notice “Authenticator” on the left side of the interface. Click on “add” and fill that form.
You will be required to enter a serial number. This serial number is found on your Android authenticator app.
Open the Android app, click on the “more” button (left bottom of the phone), “about”, “need a new serial number?”.
Scroll down and you will see the serial number and the “restore code”.
Enter them both into your form from battle.net.
You can choose to leave this option disabled, “Require an authenticator code every time you log in to the game.” This way, it will only pop up once.
I’m not sure if it will request to enter a code generated by the authenticator from time to time but I’ve seen that this is required once in 30 days if you login from a browser into the battle.net website.
You can disable the authenticator at any time.
Once last thing, you can get rid of getting locked all the time if you use an authenticator.
If you have questions, leave in the comments.