If for some reason, you are not able to install and use the API locally, you can also try the sandbox version of the API that runs in the cloud https://notebooks.esri.com/. By clicking this URL, a browser window will open with the Jupyter Notebook, where you can create your own Notebooks, run code examples, and use all of the functionality of the API. 

For an online API reference showing all modules, classes with descriptions, and examples see http://esri.github.io/arcgis-python-api/apidoc/html/index.html.

For API updates, release notes, and more, refer to https://developers.arcgis.com/python/guide/release-notes/. 

The main page for all info about the API can be found here. It´s an excellent source with lots of documentation, a user guide and API reference: https://developers.arcgis.com/python/.