I’m developing an application on Android and I want to allow users to log in with their Google account. How can I achieve this?
Sure you might want to start with this:
Third-party websites and applications can now let visitors sign in using their Google user accounts. Federated Login, based on the OpenID standard, frees users from having to set up separate login accounts for different web sites--and frees web site developers from the task of implementing login authentication measures. OpenID achieves this goal by providing a framework in which users can establish an account with an OpenID provider, such as Google, and use that account to sign into any web site that accepts OpenIDs. This page describes how to integrate Google's Federated Login for a web site or application.
https://developers.google.com/accounts/docs/OpenID
Come back when you get stuck!