Usually GUIs are based on the Observer pattern, also called Publish/Subscribe. They also use Mediator, Composite, Command, and most of the other patterns in Design Patterns. In fact, when the book first came out, people often criticised it as being a book of GUI patterns. It isn't; the patterns are much more general than GUIs. However, a large GUI framework will usually use most of the patterns.
You should get a book on GUI construction. It is a bad sign that the only pattern you mentioned was Singleton. This shows you don't understand how to construct GUIs very well. Singleton is a weak pattern, and whenever people start with Singleton, it is a sign of a bad design. -Ralph Johnson
