Tool use, a hallmark feature of human intelligence, remains a challenging problem in robotics due the complex contacts and high-dimensional action space. In this work, we present a novel method to enable reinforcement learning of tool use behaviors. Our approach provides a scalable way to learn the operation of tools in a new category using only a single demonstration. To this end, we propose a new method for generalizing grasping configurations of multi-fingered robotic hands to novel objects. This is used to guide the policy search via favorable initializations and a shaped reward signal. The learned policies solve complex tool use tasks and generalize to unseen tools at test time. Visualizations and videos of the trained policies are available at https://maltemosbach.github.io/generalizable_tool_use.