The agent/master HTTP interface is REST-like, but varies from strictly RESTful design in several ways. The endpoints used by the agent are detailed in the HTTP API reference. Note that all HTTP endpoints are preceded by the environment being used. Note also that access to each individual endpoint is controlled byauth.conf on the master.
Diagram
This flow diagram illustrates the pattern of agent-side checks and HTTPS requests to the puppet master during a single Puppet run.
See below the image for a textual description of this process, which explains the illustrated steps in more detail.