Second quantization is an important topic in postgraduate and senior undergraduate level Quantum Mechanics course. A key step in the development of the second-quantization formalism is the derivation of one- and two-body operators from the many-particle Hamiltonian and wave functions in the firstquantization language, which is usually difficult to understand for beginners. Taking the case of an assembly of identical fermions as an example, this paper provides a less ad hoc and intuitive derivation based only on the symmetrization postulate, the concept of “filling the vacuum” in the Fock space, and equivalence between the antisymmetrized many-particle wave function and the Fock state.