Understanding many-body quantum systems usually means solving the Schrödinger equation of a system of many strongly interacting particles. However, there is no analytical solution for most cases. Therefore, numerical approaches are popular in this area. One kind of the famous methods is quantum Monte Carlo. Two sampling schemes based on the Markov chain Monte Carlo introduced in this project are variational Monte Carlo (VMC) and diffusion Monte Carlo (DMC). First, we provide a brief introduction to the important Metropolis-Hastings algorithm, which is of great importance during simulation. Then, we review in detail the basic idea and principles of VMC and DMC. Throughout this project, we discuss the applications of these two methods to the first row elements and show the importance of decent trial function choices. This worksheet uses the Maple Quantum Chemistry Toolbox.