In this paper we present a paradigmatic tight-binding model for single-layer as well as multilayered semiconducting MoS2 and similar transition metal dichalcogenides. We show that the electronic properties of multilayer systems can be reproduced in terms of a tight-binding modeling of the single-layer hopping terms by simply adding the proper interlayer hoppings ruled by the chalcogenide atoms. We show that such a tight-binding model makes it possible to understand and control in a natural way the transition between a direct-gap band structure, in single-layer systems, and an indirect gap in multilayer compounds in terms of a momentum/orbital selective interlayer splitting of the relevant valence and conduction bands. The model represents also a suitable playground to investigate in an analytical way strain and finite-size effects.