Carson McDonald has posted an example of how to use the Google OAuth for Installed Apps tool to authenticate users.

I have been working on a long needed update to the Google analytics dashboard plugin for WordPress and one of the items I had on my TODO list was using Google's OAuth login instead of the old ClientLogin. Setting OAuth up for a WordPress plugin is complicated because it isn't a hosted application and as such I can't register it to get OAuth keys. That is where a special way of doing OAuth comes in called OAuth for installed apps.

He uses this OAuth library to handle the "dirty work" of the connections. With that included in the application, he shows how to - in two phases - make an authentication system that direct the user to a Google link for completing the authentication process. He points to the Google OAuth docs and playground as good resources to help you during the process.