From the outside, there's no generic method. A site can have as many (possibly obfuscated) endpoints as they wish.
You could, however, get lucky if there is an automatically generated site-map; it might just include a list of endpoints.
From the inside, it's possible. It can be labor-intensive, depending on how the site works. If you have access to the web server configuration, you can walk through it to find the endpoints.
For an Apache webserver, start with httpd.conf .
For IIS, you'll have to open the GUI and find the sites hosted by that IIS server, then find the endpoints on them.
There's been a merger, and I'm trying to address a blind spot with all the new systems and widgets. I'd like to find any/all API services available and confirm they are secured. While I could just dump dns entries and loop through them with /api/ at the end of a curl... i don't feel like that's particularly exhaustive.
I have Nessus running, but I haven't found where they have a plugin that really handles this. I did some poking around the open-source world and the search terms are generic enough that i'm not getting great results.
I want to to test a REST API and I am wondering what the best tool or approach for finding all the endpoints ist. Do you use a fuzzer? Maybe a specialized tool? Or e.g. the Intruder from the Burp Suite? Thanks for your suggestions!