We present a rigorous formulation of generalized Kohn-Sham density-functional theory. This provides a straightforward Kohn-Sham description of many-body systems based not only on particle-density but also on any other observable. We illustrate the formalism for the case of a particle-density based description of a nonrelativistic many-electron system. We obtain a simple diagrammatic expansion of the exchange-correlation functional in terms of Kohn-Sham single-particle orbitals and energies; develop systematic Kohn-Sham formulation for one-electron propagators and many-body excitation energies. This work is ideally suited for practical applications and provides a rigorous basis for a systematic development of the existing body of first-principles calculations in a controllable fashion.