<p>I'd like to start moving our application business layers into a collection of REST web services. However, most of our Intranet has been built using Classic ASP and most of the developers where I work keep programming in Classic ASP. Ideally, then, for them to benefit from the advantages of a unique set of web APIs, it would have to be called from Classic ASP pages.</p>

<p>I haven't the slightest idea how to do that. </p>

Here are a few articles describing how to call a web service from a class ASP page:
Integrating ASP.NET XML Web Services with 'Classic' ASP Applications
Consuming XML Web Services in Classic ASP
Consuming a WSDL Webservice from ASP