Reconfigurable intelligent surface (RIS) has been regarded as a revolutionary and promising technology owing to its powerful feature of adaptively shaping wireless propagation environment. However, as a frequency-selective device, the RIS can only effectively provide tunable phase-shifts for signals within a certain frequency band. Thus, base-station (BS)-RIS-user association is an important issue to maximize the efficiency and ability of the RIS in cellular networks. In this paper, we consider a RIS-aided cellular network and aim to maximize the sum-rate of downlink transmissions by designing BS-RIS-user association as well as the active and passive beamforming of BSs and RIS, respectively. A dynamically successive access algorithm is developed to design the user association. During the dynamical access process, an iterative algorithm is proposed to alternatively obtain the active and passive beamforming. Finally, the optimal BS-RIS association is obtained by an exhaustive search method. Simulation results illustrate the significant performance improvement of the proposed BS-RIS-user association and beamforming design algorithm.