I searched all the guides available and the PDFbook but cannot find the user guide for manager’s API.
Where can ik find the guide?
I am using the desktop version (21.5.20) on Windows 10.
There isn’t one 
I recommend you try searching the forum as I remember there are a few topics about API.
The API is mostly self-documenting, as long as you understand the basic concepts of a REST API.
If you access the /api endpoint you’ll see a list of businesses, and can go from there 
Username: administrator
Password: [your-administrator-password]
Should you get stuck, you could ask a few specific questions here. Or look for online tutorials explaining how a REST API works. Specifically, make sure you understand the difference between GET/PUT/POST/DELETE requests in a REST API.