Across disciplines, researchers increasingly recognize that open science and reproducible research practices may accelerate scientific progress by allowing others to reuse research outputs and by promoting rigorous research that is more likely to yield trustworthy results. While initiatives, training programs, and funder policies encourage researchers to adopt reproducible research and open science practices, these practices are uncommon in many fields. Researchers need training to integrate these practices into their daily work. We organized a virtual brainstorming event, in collaboration with the German Reproducibility Network, to discuss strategies for making reproducible research and open science training the norm at research institutions. Here, we outline eleven strategies, concentrated in three areas: (1) offering training, (2) adapting research assessment criteria and program requirements, and (3) building communities. We provide a brief overview of each strategy, offer tips for implementation, and provide links to resources. Our goal is to encourage members of the research community to think creatively about the many ways they can contribute and collaborate to build communities, and make reproducible research and open science training the norm. Researchers may act in their roles as scientists, supervisors, mentors, instructors, and members of curriculum, hiring or evaluation committees. Institutional leadership and research administration and support staff can accelerate progress by implementing change across their institutions.