While at Concur, I was the principal designer for many of the APIs, including all the ones for Concur Expense. The one most relevant to your project is the “Event Notification” API. This is a “callout” API, in that Concur acts as the HTTP client, which makes an HTTP POST to an HTTP server you specify.
The idea of this API is when an expense reports reaches the “Pre-Extraction” workflow step, which means the expense report is “approved”, it will make an HTTP POST notifying you of this event. The information in the request body allows you in turn to take action including querying for details about this expense report.
As far as configuration, you must create a configuration called an “application connector”, which provides the metadata Concur needs to be able to make the HTTP POST. Essentially, the URL and authentication credentials for the HTTP server Concur will call.
You can read about the Event Notification callout here, https://developer.concur.com/api-reference/callouts/post-event-notification.html.
This includes a sample XML for the request body.
Also, you should read the overview of callouts and application connectors here, https://developer.concur.com/api-reference/callouts/callouts-application-connectors.html.
This prescribes how to configure an application connector.
Hope that gets you started.
Chief Product Officer, Pivot Payables, Inc.