This is how I relate the three terms:


Framework is a reusable component that fulfills particular requirement. Example: J2EE framework


One needs to define an architecture for the Framework. Example: Client/Server, N-tier architecture


For a particular architecture, one will use design patterns. For example:Command,Singleton etc.


This is a overly simplified view of the relationship among these terms. There is a lot of online documentation on the web.


use Google to get more examples

Design patterns are not distinct from frameworks and architectures.
Software patterns span the range from architectural patterns, which affect overall system design (e.g., model-view-controller) at the highest end, to software idioms, which affect single lines of code (e.g., the use of for (int i = 0; i < 5; i++) rather than a while loop which does the same thing in Java) at the lowest end, with design patterns (e.g., factory, singleton) in the middle.
The book Pattern-Oriented Software Architecture: A System of Patterns by Buschmann et al. contains a much better explanation than mine.