The electrodynamic response of spin glasses (in the form of thin AuFe films) in the terahertz frequency range has been studied using backward-wave oscillator (BWO) spectroscopy (10-40 cm^-1) and optical ellipsometry (5000-33000 cm^-1) techniques at temperatures from 5 to 295 K. The room-temperature dynamic conductivity spectra of AuFe films are typical of metals and can be described within the framework of the Drude theory of conduction by free charge carriers. Changes in the microscopic parameters of charge carriers in AuFe films with increasing iron content, which are related to additional scattering of carriers on the impurity magnetic moments, have been studied on the quantitative level, including the carrier relaxation frequency and characteristic time, plasma frequency, and conductivity. It is established that the spin-glass phase at a temperature of 5 K exhibits dispersion of the conductivity in the frequency range 10-40 cm^-1, which can be related to the appearance of a mobility gap in the subsystem of free electrons involved in the RKKY interaction between magnetic centers (Fe atoms).