To start off I would use the create react app. It sets up a project and all the required settings for babel, linter and all that magic is behind a curtain. Again the documentation is fine for starting. And remember React is just the view library. If you need (global) state management look at redux or mobx, http client axios and read their documentation.
I started 3 years ago with React. Back then i just used the documentation. Now i follow Dan Abramov and other React Maintainer / developer (like Sophie Bits) on twitter and I learn a lot of internal or advanced stuff about react. I definitely would recommend following them.
There are lots of ways to connect to these APIs, but a common one with React is to a Redux middleware to do the fetching. Underneath everything, something will be using either the classic "XMLHttpRequest" or the newer "fetch api" to do the actual HTTP requests.