While it is easy to jump over Saussure's, shall we say, pure sign theory and go straight to applications or theories that grew out Saussure's discussion of sign, the four fundamentals of sign as posited by Saussure are still the critical underpinnings. These four fundamental assumptions of sign posited by Saussure, as spelled out by Columbia University's Media Center, are that sign is: diadic, arbitrary, relational, differential.
Sign Is Diadic: That sign is diadic means it is based on two: it has two inseparable parts or components. Sign may not be considered as a singular concept. The diadic parts are the signifier and that which is signified: signifier/signified. These are inseparable in experience. If we use the signifier "couch," there is a signified object or concept that is inseparably associated with it. At the same time, "couch" refers to multiple signifieds, such as your idea of Country plaid and my idea of Contemporary stuffed leather.
Sign Is Arbitrary: Signs developed through the history of language by convention since there is no innate, no natural relationship between signifier and what it signifies. For instance, there is no natural, innate relationship between "horse" and the large running beast with soulful eyes and a swishing tail. It was convention that designated this animal as "horse." This assignment by convention is a result of the arbitrary, non-natural, nature of sign. This arbitrary quality of sign leading to conventional assignment of signifier/signified applies to images as well as to language, thus the field of semiotics could be developed.
Sign Is Relational: This means that since sign is arbitrary and thus conventional (assigned by convention, or agreement within a society), when sign (sign: signifier/signified) is in a system of signs, it gains meaning from the relationship between them, just like each sign in this sentence gains meaning from each other sign. In other words, the parts work together to give meaning to each other because of how they relate to each other. This description of the relational quality of sign applies equally to language and to images.
Sign Is Differential: While sign derives meaning from relations with other signs in the same system, sign defines or differentiates by what it is not. As an example, "Dog is" derives meaning through relationship between signs while at the same time defining by differentiating from "Cat is," which it is not. A more complicated example involves both intentional and accidental ambiguity (TU Dresden) created by language and images that may be one of two things depending upon how understood or seen. Thus sign defines by differentiating while giving meaning by relation.
sing is diadic--comprised of two parts: the signifier and the signified
sign is arbitrary--there is no natural reason why a signifier is linked to a signified
sign is relational--sign only makes sense in relation to other signs in the same system
sign is differential--sign defines things by what they are not rather than by what they are (Columbia University, Media Center)