Ferdinand de Saussure (1857-1913) was a linguist, and his reformation of linguistics proved to be the starting point (along with Claude Levi-Strauss) of Structuralism. Before Saussure, linguistics had been studied historically through Etymology which is a Diachronic approach to the phenomenon (diachronic - from the root diachrony meaning "change extending through time"). Saussure argues that there must be a better way to approach language. He argues that instead of studying how a language came to mean, we should study language through a synchronic approach, that is to say the events as they exist at a particular moment.
Saussure holds that language is everywhere, all at once, complete. We can look at language as a total system of a particular moment. Saussure says diachrony (etymology) produces historical fallacy because that approach assumes that a word's historic meaning leads (causally) to its current meaning.
Instead, Saussure argues that the critic must examine the current meaning of a word. He posits that elements of language do not gain their meaning historically, rather they gain their meaning from relationships to the other language elements present at that moment. This is a of systemic view language in that the meaning of a sign results from its relationship to other signs. (Sign = Symbol). The result of this is from the identity by negation, as a sign "means" because of how it is different other signs in the system. In other words, we define signs by what they are not. He later calls this the principle of difference.
Saussure also distinguished between langue (language) and parole. Langue is possessed by everyone. It is the set of rules for combining sounds into words, words into sentences, etc. . Parole are the physical acts of speaking, occasionally called utterances or speech acts. Langue is the structure that underlies individual speech acts. To understand the individual speech acts, you have to understand the langue, the structure, from which they are created.
Saussure holds that when we look at how language works, we should examine it both syntagmatically (horizontally) and paradigmatically (vertically). Syntagmatic rules define semantic order, what words can follow other words, and what is inappropriate. Paradigmatic is the associative character of language, what we can connect, rules of similarity in meaning or sound to create a connotative spectrum of possible choice for each word in a syntagm. For instance
Syntagm: The dog sat on the mat.
So, good poetry comes from the good use of paradigmatic rules, great films come from the good use of or pushing syntagmatic rules.
Saussure holds that we don't encounter or experience anything, rather we encounter that thing's paradigmatic category. Because of this, langue is persuasive because the rhetor chooses each utterance from a paradigmatic set.
Metaphysical Assumptions of Structuralism (and thus Semiotics)...
The world is a product of our ideas (language creates reality)
The world must be seen as a logical pattern. Structuralism works on the model of the mind as a binary computer; therefore, since the mind is a part of this world, the ideas it generates must fit the logical pattern; and therefore once we see and understand the underlying structures of language we won't see the world as being so illogical.
Death of the Subject - People are products of their ideas. We, therefore, are produced by language. What we think to be free actions are not determined by our choices or decisions, but our actions are the outcome of the underlying structure of ideas. Language positions us in society. The ideology of free will makes us believe that we are in control of language when just the opposite is true. Thus, history isn't the product of human actions, but of language. We are blind to the power of language. When we become part of a linguistic community, we are written by that language.
Intertextuality -- when we communicate, we treat each other as texts. According to Saussure, no text is free of other texts, so individuals are a product of the intersections of numerous texts. As we interpret each text, each text is working to interpret (or "linguistically place") us by applying codes to us based on what we are not.
Rhetoric, then, is the set of forms through which individuals and history are expressed. Through rhetoric, language acquires its power. Rhetoric is the way language acts on us invisibly.
For the structuralist, what is important is that which is excluded. The structuralist critic tries to make the text say what the text left unsaid. Politics, sex, biases, discrimination are generally excluded from text, structuralism tries to uncover these.
As Saussure said, "You can stand against language by saying what is not typically said."
For a visual representation of Saussure's theory (and Foucault's tropological space) head to Bosch's de Saussure space.