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Hi,
I referred these below given links for one of my projects, you can refer it for your requirement.
For Google: http://phppot.com/php/php-google-oauth-login/
For Facebook login: http://phppot.com/php/facebook-open-authentication-in-php/
For both these to work you will need to register your website on Facebook/Google respectively and get the necessary details, steps for this are given in the above links.
You can use Open Auth. of Google and Facebook API for signup and login with your website.
For other services like social sharing you can use facebook API with your fb developer account