What do you call this brain-storming procedure? Is there an official name for this area of knowledge? Are there books and/or web sites about this sort of thing?
Just some keywords (& authors):
Try story telling to elicit typical user/system interactions, i.e. use cases from your users.
Find out about the important classes and their interdependencies:
Organize sessions with CRC cards: Class Responsibility Collaboration and
Do lexical analysis on business documents
Prioritize requirements / use cases in a group with MoSCoW-rules: Must / Should have / Could have / Won't have this time around
Schedule features / use cases in timeboxes
Authors:
Ivar Jacobson
Martin Fowler (Very readable and small book: UML Distilled)