It took me a little while to get this working but here is how I got Autofac working with the new ASP.NET MVC 4 Web API.
Call this setup method in Application Start event in global asax.
private static void SetupAutofac()
var builder = new ContainerBuilder();
var container = builder.Build();
GlobalConfiguration.Configuration.DependencyResolver = new AutofacWebApiDependencyResolver(container);
This sets up all API and regular controllers while injecting all the properties in them. The module (MessaagingModule) sets up the Autofac container.