Grant funder requirements often list recommended or required repositories for deposit of Open Data.
Another great option is a disciplinary repository which can aid in discovery by others in your field.
Find a repository: Registry of Research Data Repositories
Digital Commons@Hamline can also accept datasets.
Data repositories may be able to assign DOIs at deposit. Organizations and publishers can work with DataCite to assign DOIs; individuals cannot register a DOI.
Register for an ORCID ID. This helps to link all of your scholarship to, uniquely identified, you, worldwide.
Librarians can help with data sharing:
Librarians can help sustain the scholarly value of data over time through data preservation:
(Adapted and modified from University of Michigan Library, Research Data Services: https://www.lib.umich.edu/research-data-services)