How is (some) philosophy done? What examples spring to mind as classic illustrations of philosophical methodology? To get the ball rolling...
(1) Conceptual analysis, and counterexamples "intuited" through thought-experiments. E.g. JTB analysis of knowledge, and Gettier cases.
(2) The use of formal methods ("logic and language") to resolve ambiguities, and make claims clear and precise. E.g. Russell's joke. (Any better examples?)
(3) Mapping logical space, to correct mistaken assumptions -- in particular, highlighting ignored possibilities (e.g. unchanging time, or Parfit's distinction between 'equality and priority') and unseen implications (e.g. how property entails coercion).
[I think this is what most philosophy amounts to, really - which explains how philosophical progress is possible - it's simply a matter of overcoming sloppy thinking.]
(4) Perhaps a variation on #3, is just spinning a good story, i.e. offering a coherent theory that seems plausible or intellectually appealing, for lack of any more "objective" criteria. We find this in normative philosophy, I guess, whenever it appeals to the reader's "intuitions" about what's right or good (or whatever). [What would be a good example?]
What else can we add to this list?