Here is the recommended way to use Google authentication as well as a few other social integrations:
In order to use oauth2 (assuming your using MVC)
Enable the Google OpenID provider Open the App_Start\Startup.Auth.cs file and remove the comment characters in //app.UseGoogleAuthentication(); to enable Google authentication.
Under Use another service to log in, click Google. The user is then redirected to the google site where you will enter your credentials.
If you don't have this file or folder "app_start", then you probably created a 'blank' project, instead of an "internet" project when you first created the solution. It's much easier (if planning on using external logins) to select 'internet application' when you first begin. Not sure what editor your using, but Visual Studio 2012/2013 make this ridiculously easy!
If your going to use OpenID which is now the recommended way, here is a great starting point: https://developers.google.com/accounts/docs/OpenID#settingup
Lastly, if you have access to NUGET through your editor like (Visual studio) , you'll find these tasks, like adding oAuth-1/2 or openId have been made very easy..
Here is a last link that would get you off in the right direction if the above doesn't really fit your build... With a few more details, I would be more than happy to help guide you to the best solution. One thing I can say is that oauth2 IS still very relevant and used in many applications today, and you wouldn't be wrong implementing this while starting a new project today - it would be the right way to go (or at least one of the right ways to go)... Hope some of this helps and isn't just going down a path you have already been down.
Hope all is well.