"A RESTful API" is, basically, an API which employs "web URLs" as the basic format for the request: the parameters to the request appear as /slash/separated/parts/of/the/url
.
"Authentication and authorization" concerns are usually excluded from the design of such an API, although sometimes "such-and-such random string" is required to appear at a certain position in the request. (This is often simply required for "browser cache-busting.") The HTTP protocol already provides the ability to transparently send "additional information" with every request: we call these things "cookies." Web servers (Microsoft's Internet Explorer comes to mind) and Application servers often provide other ways by which they can identify clients. Thus, the design of the API itself can often "just stick to the business at hand."
Yes, you might need to design an API-call that is used to present authentication/authorization credentials ... although, in practice, this is rare. But, for the majority of your RESTful calls, you should not have to continue to be concerned with such things, that is to say, "within the actual text of the REST-strings themselves." Other means exist in the HTTP protocol by which this additional information can be conveyed to the host.