EDIT (18th September 2016): The code samples for this post have ceased to exist. This post probably won't be helpful to anyone.
So first off, what you're going to need to do is create a new ASP.NET MVC project using the "Basic" template. Create a HomeController and view for the Index method and make sure that all works nicely.
Using NuGet, go ahead and grab the AngularJS and angularjs.TypeScript.DefinitelyTyped packages. This will dump a bunch of scripts into the Scripts folder, not all of which are necessary... I just tend to add them in whenever I need them. Add in the AngularJS reference to BundleConfig.cs as needed and get it included in _Layout.html. Add the ng-app directive anywhere you want the AngularJS application to be scoped to. For me, I just use the root HTML tag.
In your Scripts folder, create a new TypeScript file. Name it whatever you want, this will be where AngularJS gets initiated from. For this tutorial i'll be using the name AngularDemo, so I'll be creating AngularDemo.ts. You'll need to add in the reference comment to load in the AngularJS typings and then go about creating the Angular application instance.
Obviously you wont see the effects of this so far since we only have the one TypeScript file, so lets add in a new TypeScript file for a basic controller. Like everything else, you can add these wherever you want, but I'll be using "Scripts/ng/controllers/TestController.ts". Using the code below, I've created a basic controller. The $scope gets passed in as a ITestControllerScope which extends ng.IScope, this allows our scopes to be type safe and fully defined.
That's really all there is to the actual setup of AngularJS in Visual Studio using TypeScript. This is really just scratching the surface of what is required to build full applications with these technologies. In the next post I'll be writing about AngularJS routing and serving templates for AngularJS to use via ASP.NET MVC.