"In order to use a native plugin you firstly need to write functions
  in a C-based language to access whatever features you need and compile
  them into a library. In Unity, you will also need to create a C#
  script which calls functions in the native library."
  from http://docs.unity3d.com/Manual/NativePlugins.html
So, basically you need to write your code in Objective-C and provide the communication between the Unity and the Native Code.
The code that you need to implement for checking Facebook APP is; 
(void) checkFacebookApp
{
   if ([[UIApplication sharedApplication] canOpenURL:[NSURLURLWithString:@"fb://"]])   
   {
      return true;
   }
}
However you need some communication between the Unity and Xcode project. So;
 class SomeScript : MonoBehaviour {
   #if UNITY_IPHONE || UNITY_XBOX360
   // On iOS and Xbox 360 plugins are statically linked into
   // the executable, so we have to use __Internal as the
   // library name.
   [DllImport ("__Internal")]
   #else
   // Other platforms load plugins dynamically, so pass the name
   // of the plugin's dynamic library.
   [DllImport ("PluginName")]
   #endif
   private static extern float checkFacebookApp ();
   void Awake () {
      // Calls the FooPluginFunction inside the plugin
      // And prints 5 to the console
      bool check = checkFacebookApp ();
   }
}