How to go about building an iPhone app that accesses a website with a custom UI?

I don't quite know how to explain this but I want to build an app that can access a website like, for example, Facebook, but I don't actually want it to be Facebook's website in the sense that I want to design the UI. There is a couple of apps like this already in the app store, one being called "Facebook开发者_JS百科 Touch HD". I have managed to get an app to access Facebook with UIWebView, but it just goes to Facebook's mobile website, obviously.

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Look at the Facebook IOS SDK.

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You probably want to fetch data from Facebook using its APIs. Facebook actually offers a library for iOS, so you may want to check it out.

In general, this applies to any site that offers an API. Usually you can use NSURLConnection to make requests to get the data you're interested in (check the specific API's documentation for details); then you have parse that data (most services output data in XML or JSON).