We present an approach to spin dynamics by extending the optical Bloch equations for the driven two-level system to derive microscopic expressions for the transverse and longitudinal spin-relaxation times. This is done for the six-level system of electron and hole subband states in a semiconductor or a semiconductor quantum structure to account for the degrees of freedom of the carrier spin and the polarization of the exciting light and includes the scattering between carriers and lattice vibrations on a microscopic level. For the subsystem of the spin-split electron subbands we treat the electron-phonon interaction in second order and derive a set of equations of motion for the 2x2 spin-density matrix, which describes the electron spin dynamics and contains microscopic expressions for the longitudinal (T-1) and transverse (T-2) spin-relaxation times. Their meaning will be discussed in relation to experimental investigations of these quantities.