To have API access to any module or object stored in Odoo, your user must be allowed to access that module information, or you must have a token that gives you API access to that information. (Both are based on the user profile) 

There are multiple ways to get your information through an API.
You can use the default Odoo XMLRPC, which has a well-defined set of rules that allow you to look up any model, filter, add the domain to the information, and limit the number of rows you can get through the call.

Or you can define your own HTTPS web service, that fetches any information and resolves it directly to the origin of the request, in any format that suits you better, whether it is a JSON structure, a CSV, or a PDF report.

The most important thing in fetching any information is to know the model's name and how to get related information. 
Usually, the record that links to other models, has an ID with the other object, and you must fetch its information on the required model. 
When there is a list of IDs, you have to fetch multiple records from the respective model to get those IDs' details

Look up the documentation if you don't know how to use the API. 
Attention it might differ a bit from version to version.