This paper will focus on electroencephalogram (EEG) signal analysis with an emphasis on common feature extraction techniques mentioned in the research literature, as well as a variety of applications that this can be applied to. In this review, we cover single and multi-dimensional EEG signal processing and feature extraction techniques in the time domain, frequency domain, decomposition domain, time-frequency domain, and spatial domain. We also provide pseudocode for the methods discussed so that they can be replicated by practitioners and researchers in their specific areas of biomedical work. Furthermore, we discuss artificial intelligence applications such as assistive technology, neurological disease classification, brain-computer interface systems, as well as their machine learning integration counterparts, to complete the overall pipeline design for EEG signal analysis. Finally, we discuss future work that can be innovated in the feature extraction domain for EEG signal analysis.