Are you accessing an APIs that already exist or creating an API for your software?
Most APIs come with some form of documentation to get you started so that is obviously the best place to start.
Before we can really help you, do you know what access method the APIs use?
OK, from what I can make out in a few minutes reading is that the APIs are http based web calls. The base URI is https://api.bookshare.org/ and you add onto the required parameters to call a particular method.
For example the docs state the ISBN search looks like this:
You would use a standard C# or VB.Net HTTPWebRequest to call the URI and a HTTPWebResponse to hold the returned data. Of course some method calls require the API key to also be sent, the written docs explained that so I don't need to copy it here.