Have a look at this blog post, that describes almost the same problem: http://android-er.blogspot.nl/2012/12/google-maps-android-api-v2-with-blank.html
If you use Google Maps Android API v2, but with a blank (gray) map displayed, and "E/Google Maps Android API(12676): Authorization failure" reported in LogCat; may be caused by a wrong API Key assigned.
In order to use Maps Android API, you have to assign a API Key in AndroidManifest.xml.
<meta-data
android:name="com.google.android.maps.v2.API_KEY"
android:value="your API Key here"/>
But there are many more sources availble that describe a similar problem: https://www.google.co.uk/search?q=google+maps+v2+blank+map&client=safari
Ofcourse I can't tell you what you did wrong, but I would suggest you take a tutorail like this one: http://www.androidhive.info/2013/08/android-working-with-google-maps-v2/ It even provides some how-to's on customization.
Or have a look at the documentation: https://developers.google.com/maps/documentation/android/start