Where are information about the API?
First I would ask which version of API he/she would want to find.
Second I would point the location (link) of the API to the user.
Third I would do an example of a certain thing to get/set through the API refering the content.
So, for example, if a user asked something about the 5.9 Rest API I would say:
The API for version 5.9 is found on this location
The content was unavailable but now it's online again! :)
So a simple example using REST API would be:
Pointing to your Bonita server on Tomcat or the "server" that the Studio provides you can easily try a rest client such as Advanced Rest Client (chrome) and configure the http request you would want. See the picture below to see an example:
A rest client is a good way to test the request you want prior to "dive" into a more abstract implementation using a Java or C# way to do the request.
Also, I agree with ttoine, the forum is a great place to make your questions!
You can find resource about the API on the documentation:
And of course, you can find many examples and answers to your questions on the Community website, just using the search tool. A lot of members are using API, ask questions, and share tips and tricks.