  We tutorially review the determinantal Quantum Monte Carlo method for
fermionic systems, using the Hubbard model as a case study. Starting with the
basic ingredients of Monte Carlo simulations for classical systems, we
introduce aspects such as importance sampling, sources of errors, and
finite-size scaling analyses. We then set up the preliminary steps to prepare
for the simulations, showing that they are actually carried out by sampling
discrete Hubbard-Stratonovich auxiliary fields. In this process the Green's
function emerges as a fundamental tool, since it is used in the updating
process, and, at the same time, it is directly related to the quantities
probing magnetic, charge, metallic, and superconducting behaviours. We also
discuss the as yet unresolved "minus-sign problem", and two ways to stabilize
the algorithm at low temperatures.
