Poststructuralism is not a single system of thought, but rather a school, or tendency. So any attempt to summarize it is bound to be a bit vague. It is also very controversial. Some say it is a meaningless language game, others that it is an immensely important contribution to human thought.
Structuralism maintained that meaning was a result of the differences between signs. The sign- actually the entire system of interrelated signs (the langue)- actually creates the meaning it claimed to signify. The world must first be categorized and broken up into bits in order to be understood, and there is no such thing as an objectively correct breaking-up. The signifier creates the signified. Concrete objects exist but categories, concepts, etc, are created by language and then treated as if they are real.
Structuralism tended to split up meaning into a system of binary oppositions. It is this because it is not that. It also held on to a few central assumptions: the speaker/writer, the reader. It was primarily linguistically oriented, though there was much important work done in structural anthropology. It would analyze a single system, but not any of the assumptions that make that system possible.
Poststructuralism holds that all systems of signs and relationships are arbitrary, and that you can never get past them to anything "real". In structuralism, meaning is arbitrary but fixed. In poststructuralism, there is no "meaning", only an endless play between signs. Insight can be gained by studying these relationships. That insight, however, is subject to further analysis. In structuralism, the structure of a langue(not the self) become the source of meaning. In poststructuralism, there is no longer a center of meaning.
Poststructuralism treats all entities involved in discourse as arbitrary. The meaning of a text comes from the reader as well as the author, and from all the intermediaries that transmit the text from one to the other. Each of these entities only exist in relation to the other- the Author needs a Reader who needs an Author. An Author only becomes an Author (as opposed to an anonymous maniac scribbling manuscripts that no one ever reads) as a result of social and economic forces. Etc.
By the way, "text" doesn't just mean a literary text to poststructuralists. Anything involving signs or relationships between things (social systems, rituals, tv programs) can be considered a "text".
So, in literary poststructuralism, not only is the book in your hands a text, but so is the system that brought the book to your hands. And all texts contain clues about the ideologies that allow them to be produced and distributed.
In general, poststructuralism works against traditional humanist/enlightenment/romantic ideas of the importance of the self, the artist, the universal. Signifiers do not refer to signifieds, only other signifiers. There is no certain identity.
The infamous deconstructionism is a poststructuralist mode of analysis, and poststructuralism itself is a part of the general postmodern direction.
Important thinkers considered at least partly poststructuralist include Jacques Derrida, and Roland Barthes.