With the increasing demand for spectrum efficiency and energy efficiency, reconfigurable intelligent surfaces (RISs) have attracted massive attention due to its low-cost and capability of controlling wireless environment. However, there is still a lack of treatments to deal with the growth of the number of users and RIS elements, which may incur performance degradation or computational complexity explosion. In this paper, we investigate the joint optimization of user scheduling and precoding for distributed RIS-aided communication systems. Firstly, we propose an optimization-based numerical method to obtain suboptimal solutions with the aid of the approximation of ergodic sum rate. Secondly, to reduce the computational complexity caused by the high dimensionality, we propose a data-driven scalable and generalizable multi-agent deep reinforcement learning (MADRL) framework with the aim to maximize the ergodic sum rate approximation through the cooperation of all agents. Further, we propose a novel dynamic working process exploiting the trained MADRL algorithm, which enables distributed RISs to configure their own passive precoding independently. Simulation results show that our algorithm substantially reduces the computational complexity by a time reduction of three orders of magnitude at the cost of 3% performance degradation, compared with the optimization-based method, and achieves 6% performance improvement over the state-of-the-art MADRL algorithms.