How do I know which metadata elements to include in the body of a request to the DataCite JSON REST API?

The DataCite REST API uses a standard JSON API format based on https://jsonapi.org/. The elements correspond to the DataCite metadata schema. The best way to see the properties in JSON is to look at the response from a DOI request.

Example:
https://api.test.datacite.org/dois/10.70126/t70h-qt35?affiliation=true

The API reference also lists all the possible property options for the REST API. In most cases it is best to start from the REST API guide, make the basics, then work with the metadata schema to add mandatory/recommended fields as appropriate (e.g. Identifier).

There is also an OpenAPI specification available in Github which describes the REST API.