What needs to be done on each social network to get your website's pages to be presented properly.
Twitter makes it very clear on their website. There are a few different types of cards and it involves putting <meta>
tags on each of your pages for the relevant info.
Facebook is a little more restrictive on what works for them. You need to create an app for your webpage to be able to post Open Graph stories
These two are the more prominent ones but there are a couple of others.
Google works in a way similar to Twitter in that you put in some metatags with schema.org info or Open Graph tags containing the info on your website. https://developers.google.com/+/web/snippet/article-rendering