How to open Settings programmatically like in Facebook app?

You can't, there is no API call to do this.

Only system dialogs, dialogs from Apple Frameworks, can open the settings app. In iOS 5 there was a app url scheme to open the system dialog but Apple removed it later.

---

With the coming of iOS 8 you can open the settings dialog on your apps page.

if (&UIApplicationOpenSettingsURLString != NULL) {
   NSURL *url = [NSURL URLWithString:UIApplicationOpenSettingsURLString];
    [[UIApplication sharedApplication] openURL:url];
}
else {
  // Present some dialog telling the user to open the settings app.
}

On iOS 8 you can open Settings programmatically!

Here is the code:

- (void)openSettings
{
    BOOL canOpenSettings = (&UIApplicationOpenSettingsURLString != NULL);
    if (canOpenSettings) {
        NSURL *url = [NSURL URLWithString:UIApplicationOpenSettingsURLString];
        [[UIApplication sharedApplication] openURL:url];
    }
}

If your app has it’s own settings bundle, the settings will be opened showing your app’s settings. If your app does not have a setting bundle, the main settings page will be shown.