Today's students are tomorrow's researchers, and so intentionally integrating reproducibility into the curriculum will be crucial in promoting reproducible practices in the long term. Teaching students to work reproducibly starts with providing them with the skills to document their work so that any other researcher can reproduce their results with the materials provided by the student.
One way to accomplish this is to design an assignment that minimally requires students to submit their final report, the data files they used in their analysis, and the code files (e.g. R or Python) that they used to generate the results contained in their report.
Another popular method for teaching reproducible research is to have an assignment that requires students to reproduce or replicate some or all of the results of a published journal article.
A number of educators are using GitHub to share their course materials, which allows others to easily remix and adapt the resources in their own teaching.