The rising number of polarized observations of relativistic sources necessitates a correct theory for proper model fitting. The equations for general relativistic (GR) polarized radiative transfer are derived starting from the Boltzmann equation and basic ideas of general relativity. The derivation is aimed at providing a practical guide to reproducing the synchrotron part of radio and submillimetre emission from low-luminosity active galactic nuclei (LLAGNs), in particular Sgr A*, and jets. A recipe for the fast exact calculation of cyclo-synchrotron emissivities, absorptivities, Faraday rotation and conversion coefficients is given for isotropic particle distributions. The multitude of physical effects influencing simulated spectra is discussed. The application of the prescribed technique is necessary to determine the black hole spin in LLAGNs. The observations of total flux, linear and circular polarization fractions, and electric vector position angle as functions of the observed frequency could substantially constrain the absolute value and orientation of spin.