Machine Learning algorithms can support the work of lithofacies classification using well logs. A wide range of automatic classifiers is available for that purpose. In order to investigate about the accuracy and the effectiveness of different methods, I compare six supervised learning algorithms. Using multiple data sets of composite logs, I discuss the entire workflow applied to two wells. The workflow includes the following main steps: 1) statistical data analysis; 2) training of six classification algorithms; 3) quantitative evaluation of the performance of each individual algorithm; 4) simultaneous lithofacies classification using all the six algorithms; 5) results comparison and reporting. Using cross-validation tests and confusion matrices, I perform a preliminary ranking of the six classifiers. Although the different algorithms show different performances, all the methods produce mutually consistent classification results. Consequently, I set a comprehensive workflow that includes all the classifiers working in parallel in the same Machine Learning framework. I show through tests on real data that this "systemic approach" allows efficient training of many algorithms, easy comparison of the results, and robust classification of multiple well data. This methodology is particularly useful when quick lithofacies classification/prediction is required for making real-time decisions, such as in case of well-site geological operations.