The POCOs created by EF are supposed to be used as your model. The general idea is that you have EF providing access to your database. You query EF using LINQ and/or extension methods and end up with an object or collection of objects that you display on your UI by binding them in WPF. That is of course if you're using WPF as opposed to the older WinForms. I can tell you from experience that it's a very streamlined process once you become familiar with the technologies. That's how a very basic setup would work.
A more advanced way of going about it is adding architectures like Model-View-ViewModel (MVVM) and possibly the repository pattern into the mix at which point you get better separation of code and presentation at the cost of increased complexity.
I don't know what flavor of MVC you're using and how it can be made to intermingle with the above, but if you want to know more about how EF was envisioned to work you should look into the technologies I've listed above.