Unit testing a Web API controller is just like unit testing anything else. Create a new controller instance using stub dependencies, execute the controller action method, assert on what comes out.
var stubDependency = MockRepository.GenerateStub<IDependency>();
var controller = new MyController(stubDependency);
var result = controller.MyAction("some-input");
Assert.Equal("expected", result);
Are you thinking about something different? If so, perhaps some additional context in your question would help.
-T