There are many ways a site or web app can integrate with social media platforms such as Facebook, Twitter, Flickr, Pinterest and more.
How you do this depends entirely on what you want to acheive. You can publish new content on your site to social media sites, or you can pull in content from social media to display on your site. You can allow your users to login to your site using their social media login details if you wish. Most commonly you would want your users to share content that they like to their social media to direct traffic back to your site. We can create a system which fulfills all of your requirements.