Unless your notebook is using locally stored data, it is self-contained – text, code and results – within a single file. Even if there are additional files on the side (libraries, data files), it can be easily published with one of the generic or open-science-focused services.
Publishing on GitHub
GitHub is a repository site with multiple extensions on top. The step-by-step procedure to use it for publishing notebooks is documented on their own site: https://reproducible-science-curriculum.github.io/sharing-RR-Jupyter/
The Interactive Notebooks Service has a Git extension 
, which makes the work with git , including management of remote repositories, as easy as possible.
Publishing with Zenodo
Zenodo is an open repository of outputs originating from research, which is mostly funded by European Commission programmes. Again, the publication procedure is documented on their side: https://help.zenodo.org/docs/get-started/quickstart/
Replaying Published Notebooks
Naturally, for repeatability, it is also important to be able to re-run the published notebooks. This can be done in one's own notebooks environment, or with Binder. The procedure of using Binder for replaying published notebooks is again documented in community-driven resources.