Strong Coulomb interaction in atomically thin transition metal dichalcogenides makes these systems particularly promising for studies of excitonic physics. Of special interest are the manifestations of the charged excitons, also known as trions, in the optical properties of two-dimensional semiconductors. In order to describe the optical response of such a system, the exciton interaction with resident electrons should be explicitly taken into account. In this paper, we demonstrate that this can be done in both the trion (essentially, few-particle) and Fermi-polaron (many-body) approaches, which produce equivalent results, provided that the electron density is sufficiently low and the trion binding energy is much smaller than the exciton one. Here, we consider the oscillator strengths of the optical transitions related to the charged excitons, fine structure of trions, and Zeeman effect, as well as photoluminescence of trions illustrating the applicability of both few-particle and many-body models.