You double click on your iOS storyboard, it opens, and then nothing. A blank screen or maybe an error if you're lucky. There are two steps to follow to make storyboards load.
1. Connect to Mac
Make sure Xamarin is connected to a Mac. To load the storyboard Xamarin needs to talk to the Mac, if you're not connected it ain't going to load.
2. Make sure you have write permissions
To load a storyboard read-only permissions is not enough. Xamarin needs write permissions too. This means if you are using source control such as TFS you will need to check out the file before you can view it.
That's it. Follow these two steps and you should be able to load iOS storyboards in Visual Studio without any problems.