Density Functional Theory is one of the most successful approaches for computing the electronic structure of materials and is currently used to study thousand-atom systems today. The goals of this tutorial are two-fold. First, I will present the basic equations and ideas behind the solution of the many-body electronic Schrodinger equation through the Density Functional approach that leads to the Kohn-Sham equations. I will then discuss the most commonly used approximations and how they translate into the two main types of numerical algorithms used to solve the Kohn-Sham equations. In the second part of this talk, I will outline the major computational components of plane wave DFT codes, which represent the dominant approach for the simulation of materials science problems. Finally, I will discuss some of the computational challenges, including parallelization, of the resulting large-scale simulations.