Well I think the other answers will help you understand the use of the interface to abstract logic in different concrete classes, I also think you can accomplish something similar to what you want using the refactoring tools built into VS.
Define your class...
public class Person
{
public int ID { get; protected set; }
public string FirstName { get; set; }
public string LastName { get; set; }
public string FullName { get { return FirstName + " " + LastName; } }
}
Then right click, select Refactor -> Extract Interface.
This will create a separate file containing the interface for the definition of the class, you could then mold the interface and implementing classes accordingly.
Extracted Interface:
interface IPerson
{
string FirstName { get; set; }
string FullName { get; }
int ID { get; }
string LastName { get; set; }
}