Reconfigurable Intelligent Surfaces (RISs) are recently attracting a wide interest due to their capability of tuning wireless propagation environments in order to increase the system performance of wireless networks. In this paper, a multiuser wireless network assisted by a RIS is studied and resource allocation algorithms are presented for several scenarios. First of all, the problem of channel estimation is considered, and an algorithm that permits separate estimation of the mobile user-to-RIS and RIS-to-base stations components is proposed. Then, for the special case of a single-user system, three possible approaches are shown in order to optimize the Signal-to-Noise Ratio with respect to the beamformer used at the base station and to the RIS phase shifts. Next, for a multiuser system with two cells, assuming channel-matched beamforming, the geometric mean of the downlink Signal-to-Interference plus Noise Ratios across users is maximized with respect to the base stations transmit powers and RIS phase shifts configurations. In this scenario, the RIS is placed at the cell-edge and some users are jointly served by two base stations to increase the system performance. Numerical results show that the proposed procedures are effective and that the RIS brings substantial performance improvements to wireless system.