How can I make my app to appear in Share activity list of Safari, photos, etc.? I would like to let people share link/image or text through my app like they do on facebook.
Facebook/Twitter etc. are available in default UIActivityType list, but how do other apps like Pinterest, Zomato, etc. acheive this?
This is new functionality implemented in iOS 8 and up (and OS X 10.10 and up). It's called Extensions. Extensions lets apps leave their Apple sandbox and access other parts of the OS, including notification center and share sheets. Apple puts it like this:
Starting in iOS 8.0 and OS X v10.10, an app extension lets you extend custom functionality and content beyond your app and make it available to users while they’re using other apps or the system. You create an app extension to enable a specific task; after users get your extension, they can use it to perform that task in a variety of contexts. For example, if you provide an extension that enables sharing to your social sharing website, users can use it to post a remark while surfing the web. Or if you provide an extension that displays current sports scores, users can put it in Notification Center so that they can get the latest scores when they open the Today view. You can even create an extension that provides a custom keyboard that users can use in place of the iOS system keyboard.
There are several different types of extensions, including Apple Watch apps. You can view all those types in the Apple documentation.
To get started building extensions, here are some resources: