The API is documented here. Since it is an OpenAPI you can import this URL into Postman or your favorite API testing tool to get a feel for what is available. But SSRS is divided into 2 pieces: management and execution. The API appears to only be the management side so you can create and modify reports but not execute them.
To render a report you can either use the SOAP service ASMX or the URL access approach. Personally I prefer the SOAP service as it is more flexible. You would use Connected Services to point to the ASMX endpoint. Visual Studio auto-generates a wrapper client that you can then use. We have this wrapped in a reusable library for our company so not every project needs a connected service endpoint. After that you simply need to call the Render method on the server client with the report information, optional credentials and rendering options you have.