Light-matter interaction plays an important role in the implementation of unique application of quantum optics, such as quantum memory protocol. In recent years, the physical implementation of quantum interfaces between light and matter in free space has initiated a very active research. In spite of significant advances, the efficiency of demonstrated quantum memory protocols is not extremely high, which is issued with problems of achievement of high-efficient light-matter coupling. Interfacing guided light with atoms has therefore been foreseen as a promising alternative approach, enabling increase the light-matter coupling as well as obtain a large optical depth. A significant role in such kind of interaction processes belongs to the evanescent field, which appears due to a small diameter of the nanofiber (less then light wavelength) that leads to more effective light-matter coupling in the evanescent field area. In the present work we consider experimental demonstration and theoretical description of the quantum memory protocol for the nanofiber guided light interfacing with 133Cs atoms, cooled in a magneto-optical trap. The nanofiber guided signal field interacts with atoms on atomic transition of D2-line. The control field is applied on resonance to atomic transition and creates the transparency window in accordance with the electromagnetically induced transparency (EIT) mechanism. We consider the light interaction process with all hyperfine atomic structure and discuss the influence of the nanofiber on the light interaction process with the atomic system.