Everyone loves the Services module. It allows you to easily create API endpoints for Drupal's core features, permitting you to interact with Drupal from external applications. It also very easily extended.
Among its many default resources, Services offers a user.login method that allows external applications to authenticate via Drupal. I'm going to share a quick snippet that will permit you to extend Services so that it allows your users to login via Facebook (leveraging the FBOauth module).
Start by downloading and enabling Services and Fboauth. Then, create a custom module to house your code. Your module's info file should specify services and fboauth as requirements.