In production, you don’t choose yourself. You create a service account instead to avoid problems in the future. If you use yourself and leave the company, the process starts to fail when your Salesforce account is disabled.
After defining the auth provider, Salesforce generates several URLs. Use the Test-Only Initialization URL to test your connection with the social network.
If it works, you get the Facebook login page.
Log in to the Facebook page.
You’re redirected to Salesforce, where you see the XML information that Facebook sent us.
Log In with Facebook
To confirm your change, return to your private (incognito) browser and reload the login (customers Communities URL)page. Check that the Facebook icon appears on the login page.
This blog is very useful to learn about the Authentication Provider Setup.