We've posted our episode (here) on a historical progression in thought that is still responsible for a lot of the hard-to-read parts of continental (mostly French) philosophy today.
First, we read Part I and Part II, Chapter IV of Ferdiand de Saussure's Course in General Linguistics(read it online here), published posthumously in 1916 (it's basically lecture notes by his students; Saussure didn't write it down himself in full). This text sharply distinguishes structural analyses of a particular language at a particular time with analyses of linguistic changes over time.
This was read by French structuralists like Claude Levi-Strauss as a blueprint for talking about structures in other cultural creations, so we read a short essay by him: "The Structural Study of Myth" (1955), which you can find online here, or you can pick up a used copy of the compilation in which it appeared,Structural Anthropology,which will help you further connect the dots between Saussure and Levi-Strauss.
Finally, we read a short essay by Jacques Derrida, "Structure, Sign, and Play in the Discourse of the Human Sciences" (1966), which you can read here, where he discusses Levi-Strauss and characterizes the limitations of structuralism, thereby laying out his own post-structuralism. This essay was published in Writing and Difference(1966).
The transition here is a funny one: Saussure didn't see himself as a philosopher at all. He was a linguist, and from what I've read, his linguistics is pretty obsolete at this point. What stuck (and what we discussed) was the basic picture he sketched of the relation of words to thought. He saw thought as blurry and formless before language comes along to carve some particular concepts out from others, and these concepts can really only be understood in opposition to other concepts. There's no question, as you might attribute to Frege or early Wittgenstein, of language being based ultimately on pointing out some psychologically distinguished object in the world and saying "tree." Instead, for Saussure it's language that creates the concept. Now, whether it does so entirely arbitrarily is not really something Saussure is concerned with, but the epistemological position that it does--that language in effect creates our reality--is what many of his successors ran with. Since words and concepts, then, don't have any ultimate grounding in the world, the only way they can be understood is through contrast with other words and concepts according to this view. This is the root of Derrida's famous concept différance, which is among other things "the notion that words and signs can never fully summon forth what they mean, but can only be defined through appeal to additional words, from which they differ."
Levi-Strauss picked up on the idea of a language as an unconscious group production whose elements are distinguished by difference and (along with a number of other structuralist writers) extended this idea to other cultural products: they're all semiotic systems (systems of meaning). In analyzing the myth of Oedipus (which is worth your reading, we didn't really recap the analysis on the 'cast), he makes a chart with underlying, opposing (meaning here's where "difference" comes in) themes in the myth that demonstrate conflicts in what you might think of as the unconscious ideology of the culture. Levi-Strauss saw this sort of analysis as getting at timeless qualities of myth, and ultimately structures of the human mind.
The Derrida essay (which was the early work that really got him famous) was presented at a conference meant to honor Levi-Strauss but in effect rejected Levi-Strauss's scientific pretensions, largely using quotes from Levi-Srauss himself. Derrida thought that there was no reason to privilege Levi-Strauss's interpretation of the myth over any of the extant versions of the myth: they're all just stories related to each other. For Derrida, meanings don't lead to some knowledge of deep human nature, but just to other meanings, other words, other stories. The chain never terminates in something extra-linguistic; we live in a world of language and nowhere else. Don't expect a full-on explanation of Derrida's deconstruction project in this discussion; we got as far as the critique of Levi-Strauss, and that's it.