On the AndroidHive site there's a recent tutorial (plus screencast) about combining PHP, MySQL and SQLite to act as the backend authorization for your Android application.

In my previous article Android Login and Registration Screen Design i explained designing the login and registration interfaces, but it has no functionality. In this tutorial i am explaining how to build complete login and registration system in android using PHP, MySQL and SQLite. Also this tutorial covers how to build simple API using PHP and MySQL.

The tutorial walks you through each step of the process:

• Creating MySQL Database and Tables
• Building PHP API Classes
• Starting Android Project
• Making the JSON Parser, SQLite Database Handler and User Functions Classes
• Designing the Screens
• Switching between Activities
• Finally Updating AndroidManifest.xml

If you want to get started quickly, you can just download the final result and go.