We investigate conformational dynamics and phase transitions of surfactant molecules confined in the layered galleries of the organo-modified, natural polysilicate clay, magadiite. We have shown that our approach to studying this class of materials is capable of delivering detailed information on the molecular mobility of the confined molecules. From the analysis of the measured heteronuclear dipolar couplings, the orientational order parameters of the C-H bonds along the hydrocarbon chain have been determined. Three phases have been observed in the nanocomposite, characterized by distinct dynamical states of the surfactant. At room temperature, restricted mobility of the molecules led to the adoption of an essentially all-trans conformation by the chains. This behavior can be described by a model incorporating small-angle wobbling around the long molecular axes of the chains. Upon heating, dynamic transformation takes place, resulting in a rotator type solid phase where molecules in extended all-trans conformations undergo fast and unrestricted rotation about their respective symmetry axes. The second phase transition is associated with chain melting and the onset of translational dynamics and results in an essentially liquid-crystalline-like state of the organic component. The mobility of the surfactant is one of the key factors facilitating the efficient penetration of macromolecules in the process of preparing of polymer/organoclay nanocomposites. The exploration of dynamic properties of the functionalizing organic layer should provide important input into the improved design of new organic-inorganic hybrid materials.