How to implement Social Media in Apps?

I have successfully made a game named ReAcsion. However, I never added Game Center, or any score sharing method to it. Now that I'm working on my second game, I would like to know how you can implement GameCenter, and Google Play connect (or watever it is called). This way, when someone gets a high score, they can compare it to their friends. They should also be able to post to social media like instagram and twitter. How can I do this? is there anyway i can do it where i don't have to pay money for a plugin?