In a tutorial posted to his site Matt Stauffer shows you how to integrate Laravel with GitHub's authentication to link a user's profile to your application, made possible through the Socialite package.

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. I'm working on a new little micro-SaaS that is purely dependent on GitHub in order to operate, so there's no reason to set up any user flow other than just GitHub.

He starts with just a bit of insight into the overall flow of an OAuth connection with an application (which this is) and the pieces involved. Next he helps you get Socalite installed and working with your Laravel application. With this in place he shows you how to create a simple GitHub application and configure your Laravel instance with the provided client ID/secret and redirect URL. He adds in some routes to handle the two page requests and the controller methods to process the input. He makes a simple "users" migration to hold user information and a model to match. Finally he shows the result, stepping through the authorization flow, complete with screenshots.