The relaxation rate in Nb-doped strontium titanate involving different scattering channels is investigated theoretically. It is demonstrated that the total relaxation rate in SrTi _1-xNb _xO ₃ is provided mainly by two mechanisms. The Baber electron-electron scattering with participation of both Coulomb and phonon-mediated electron-electron interactions provides the T2 dependence of the relaxation rate. The scattering on the potential landscape caused by impurities is responsible for the residual relaxation rate at low temperatures. A good agreement with experiment is achieved accounting for all phonon branches in strontium titanate, both the optical and acoustic phonons. It is shown that the effective electron-electron interaction can be attractive in strontium titanate, and provides superconductivity at low temperatures and Fermi-liquid response in a wide range of temperatures. Thus our microscopic model supports the notion that superconductivity and Fermi-liquid properties of n-type SrTiO ₃ have a common origin.