This paper in a didactic way, presents an introduction to quantum computing where some quantum formalisms are analyzed to finally address Grover's algorithm. It is widely known that this algorithm is one of the key algorithms in quantum computing, being its ability to explode successfully the superposition principle one of the reasons. In addition, this algorithm can be used for both locating efficiently a specific element in a cluttered database and solving certain problems when it is difficult finding a proper solution, but at the same time it is very simple to try with possible candidates. Finally, a simulation of this algorithm is carried out and the results are compared with other classical algorithms to illustrate the significant potential advantages of quantum computing.