Structuralism is essentially a meta-theory, rather than a theory of literature. That is, it is not really about art itself, but about approaches to art. The big name here is Claude Levi-Strauss, who started it all by looking at mythology in terms of structural units, called mythemes, and at the relationships between these mythemes. Basically, he says that we can look at any myth as a whole bunch of mythemes tacked together. So, the Oedipus myth contains mythemes of "The Young Man with Mysterious Origins," "The Encounter on the Road," "Self-Mutilation," and a whole bunch of others, depending on which particular telling of the tale we're dealing with. According to Levi-Strauss, we can look at a whole bunch of different tellings and put together a pretty good idea of what the whole myth really says, and that by looking at how all these mythemes go together, we can also understand a lot about mythology, since the same mythemes keep showing up in different cultures all over the world.
However, (and this is a big "however") the Post-Structuralists come in with a very important objection. What Levi-Strauss does not seem to realize is that the mythemes he talks so much about are simply arbitrary (although unavoidable) abstractions out of an aesthetic manifold (see Marx's definition of thought), and that they are as culturally determined as any myth. This sort of undercuts any gestures toward universality that Structuralists might be able to make.