The aim of this work is to provide a didactic approximation to memetic algorithms (MAs) and how to apply these techniques to an optimization problem. MAs are based on the synergistic combination of ideas from population-based metaheuristics and trajectory-based search/optimization techniques. Most commonly, MAs feature a population-based algorithm as the underlying search engine, endowing it with problem-specific components for exploring the search space, and in particular with local-search mechanisms. In this work, we describe the design of the different elements of the MA to fit the problem under consideration, and go on to perform a detailed case study on a constrained combinatorial optimization problem related to aircraft landing scheduling. An outline of some advanced topics and research directions is also provided.