Recently i’ve noticed many news sites creating new application on facebook for sharing articles.
something like mini-site of the website inside facebook platform.
I.e Washington post application.
I’ve tried to find the how-to-do on facebook developers center but couldn’t.
You’re talking about Open Graph actions here. Apps can define objects, and actions that can be performed on them (although fo reading an article you now have to use the build-in types), and then publish these actions on a user’s behalf.
Please familiarize yourself with the concept, start reading here: https://developers.facebook.com/docs/opengraph/