Most psychiatric disorders are associated with subtle alterations in brain function and are subject to large inter-individual differences. Typically the diagnosis of these disorders requires time-consuming behavioral assessments administered by a multi-disciplinary team with extensive experience. Whilst the application of machine learning classification methods (ML classifiers) to neuroimaging data has the potential to speed and simplify diagnosis of psychiatric disorders, the methods, assumptions, and analytical steps are not currently opaque and accessible to researchers and clinicians outside the field. In this paper, we describe potential classification pipelines for Autism Spectrum Disorder, as an example of a psychiatric disorder. The analyses are based on resting-state fMRI data derived from a multi-site data repository (ABIDE). We compare several popular ML classifiers such as support vector machines, neural networks and regression approaches, among others. In a tutorial style, written to be equally accessible for researchers and clinicians, we explain the rationale of each classification approach, clarify the underlying assumptions, and discuss possible pitfalls and challenges. We also provide the data as well as the MATLAB code we used to achieve our results. We show that out-of-the-box ML classifiers can yield classification accuracies of about 60-70%. Finally, we discuss how classification accuracy can be further improved, and we mention methodological developments that are needed to pave the way for the use of ML classifiers in clinical practice.