Electroencephalogram (EEG) signals reflect the activities or electrical disturbances in neurons in the human brain. Therefore, these signals are vital for diagnosing certain brain disorders. This study mainly focused on the diagnosis of epilepsy and autism spectrum disorders (ASDs) through the analysis and processing of EEGs. In this study, artifacts were removed from the EEG datasets using Independent Component Analysis and were filtered using a fifth-order band-pass Butterworth filter to remove interference and noise. Next, new methods were used to extract the features of EEGs using common spatial pattern (CSP). It is known that conventional CSP uses variance. However, here the use of entropy, energy, and band power with CSP was proposed to extract features of EEGs. Then, in our investigation, four techniques were employed for classification, namely, linear discriminant analysis, support vector machine, k-nearest neighbor (KNN), and artificial neural network, with the aim of comparing the proposed methods and recommending the optimal combination for the diagnosis of epilepsy and ASDs. Finally, the effects of segment length, frequency band, and reduction number on the results were investigated. Two EEG datasets were employed to verify the proposed methods: the King Abdulaziz University dataset (for ASD) and the MIT dataset (for epilepsy). The results indicated that the extracted features based on CSP and band LBP produced the best performance and that the combination of CSP-LBP-KNN provided the best performance with average classification accuracy of approximately 98.46% and 98.62% for diagnosing ASDs and epilepsy, respectively.