A methodology of including QCD next-to-leading-order corrections in the quark-gluon Monte Carlo shower is outlined. The work concentrates on two issues: (i) constructing the leading-order parton-shower Monte Carlo from scratch, such that it rigorously extends collinear factorization into the exclusive (fully unintegrated) one which we call the Monte Carlo factorization scheme; (ii) introducing next-to-leading-order (NLO) corrections to the hard process in this new environment. The presented solution is designed to be extended to the full NLO-level Monte Carlo, including NLO corrections not only in the hard process but in the whole shower. The issue of the difference between the factorization scheme implemented in the Monte Carlo (MC) solution and the standard scheme is addressed. The principal MC implementation is designed for the electroweak boson production process at the LHC, but in order to discuss universality (process independence), the deep inelastic lepton-hadron scaterring is also brought into the MC framework.