The reconfigurable intelligent surface (RIS) technology is ushering in a new paradigm for wireless communication systems. It provides an accessible way for controlling the interaction between electromagnetic waves with the propagation medium. As a consequence, there are currently a wealth of works investigating several aspects of the RIS, such as its construction materials, components, and related channel models, to name a few. One particularly important aspect, however, is the configuration of the RIS elements or reflectors. Assuming that each RIS element is represented by a phase-shift, then the objective of the RIS configuration is to determine the optimum phase-shift combination that maximizes the channel capacity. To this end, we propose a data-driven configuration method for the RIS. In light of the remarkable results recently obtained by machine learning algorithms in wireless communications, it leverages neural network (NN) architectures to configure the RIS phase-shifts. In this work, we investigate the RIS configuration under continuous and discrete phase-shifts, also considering the user equipment (UE) mobility. Numerical results demonstrate that the proposed NN promotes far less reconfigurations of the RIS, consequently reducing the configuration overhead. Moreover, the proposed NN also outperforms other state-of-the-art methods in the mobility scenario.