I created an ASP.NET MVC 4 Internet Web Application using Simple Membership db for storing users, roles and profiles.
In my app I created a Web API controller that will
That depends on how you're coding your app, but basically, you'll use http protocol for this. Take a look at ASP.NET MVC - HTTP Authentication Prompt and http://www.piotrwalat.net/basic-http-authentication-in-asp-net-web-api-using-membership-provider/
You should make another api, that checks the authentication from the Windows 8 app or Windows.
If its pass successfully from the authentication, then only you have to show user list to the client.