In this tutorial, Matt Stauffer shows you how to implement Laravel Socialite and Github as a login system:
Laravel’s Socialite package makes it simple to authenticate your users to Facebook, Twitter, Google, LinkedIn, GitHub and Bitbucket. You can authenticate them for the purpose of connecting their pre-existing user account to a third-party service, but you can also use it as your primary login mechanism, which we’ll be talking about here.
He starts off covering the basics of oAuth, and leads into the installation, creating a Github app, and then the controller setup, database, and routes. He also mentions Adam Wathan’s Eloquent oAuth Package as a good choice if you only want the “login”.