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In cognitive neuroscience research, computational models of event-related potentials (ERP) can provide a means of developing explanatory hypotheses for the observed waveforms. However, researchers trained in cognitive neurosciences may face technical challenges in implementing these models. This paper provides a tutorial on developing recurrent neural network (RNN) models of ERP waveforms in order to facilitate broader use of computational models in ERP research. To exemplify the RNN model usage, the P3 component evoked by target and non-target visual events, measured at channel Pz, is examined. Input representations of experimental events and corresponding ERP labels are used to optimize the RNN in a supervised learning paradigm. Linking one input representation with multiple ERP waveform labels, then optimizing the RNN to minimize mean-squared-error loss, causes the RNN output to approximate the grand-average ERP waveform. Behavior of the RNN can then be evaluated as a model of the computational principles underlying ERP generation. Aside from fitting such a model, the current tutorial will also demonstrate how to classify hidden units of the RNN by their temporal responses and characterize them using principal component analysis. Statistical hypothesis testing can also be applied to these data. This paper focuses on presenting the modelling approach and subsequent analysis of model outputs in a how-to format, using publicly available data and shared code. While relatively less emphasis is placed on specific interpretations of P3 response generation, the results initiate some interesting discussion points. [ABSTRACT FROM AUTHOR]