In recent years, the growth of low-cost, non-invasive and portable electrophysiological systems that record and process brain signals, has increased. As a result, Brain Computer Interface (BCI) systems are becoming more and more accessible to the research community, serving various applications and needs, in contrast to earlier times, when these systems were more expensive, a lot more complex in their use, while their utilization focused particularly on health and medical applications. In this paper, information, on BCI systems, is provided and then, the overall procedure that has been followed, is described for the analysis and classification of signals acquired from an ElectroEncephaloGram (EEG). More specifically, there is a detailed description of the procedure of acquiring the data (i.e., EEG signals) from the brain as well as the steps for pre-processing and enhancing the recorded signals. Furthermore, some of the most common feature extraction techniques, along with associated classification algorithms, are combined and their performance is evaluated in terms of accuracy. The best combination is used for demonstrating the control of a flying drone both in simulated and real-world scenarios.