Update: my blog post The lie of the API details the issues with current APIs.
Background: I'm a researcher in semantic hypermedia, at the moment comparing different APIs for accessing metadata for human and machine consumption.
Story: I am browsing a cultural website and want to retrieve the metadata of the object I'm looking at in a machine-readable format. The steps below are the actual steps that I've undertaken on different sites.
I'm looking at the object http://collection.cooperhewitt.org/objects/35460799/.