This review article explores the basic principles and some practical applications of Density Functional Theory (DFT) in computational materials science, highlighting its significance in predicting and analyzing the electronic, structural, thermodynamic, optical, electrical, and magnetic properties of materials. We begin with discussing the fundamental principles of DFT, including the Hohenberg-Kohn theorems and the Kohn-Sham equations, which provide the framework for solving quantum mechanical equations for many-body systems. The review then explores further approximations used to make these complex calculations feasible, such as the Local Density Approximation (LDA), Generalized Gradient Approximation (GGA), and hybrid functionals. We also mention and classify some popular DFT-based software packages, such as WIEN2k, Quantum ESPRESSO, VASP, ABINIT, and CASTEP, according to their basis set types, computational requirements, and typical use cases. The discussion leads to a focus on WIEN2k, considering the balance of its accuracy and cost, and concluding its choice as a preferred software for our future research in materials science using computational methods.