In the case of the Engine Yard API, there's actually quite a lot of information that we can get from the API overview:

• It's an authenticated HTTP API
• The authentication token can be passed in either as part of the query or as the X-EY-TOKEN request header
• From this page, we know that the GET, POST, PUT, and PATCH HTTP verbs are used
• We know that the API can both accept and serve the application/json MIME type
• From the sidebar, we can see that there are a good number of endpoints off of the API root

Taking a look around at some of those endpoints, we learn even more about this specific API:

• The API is versioned
• The desired API version is specified as part of the Accept request header: application/vnd.engineyard.v3+json
• The DELETE HTTP verb is also used in this API