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Use it. Sounds simplistic but it's one the best, fastest teachers. Think up a sample project like a more advanced todo app and try to build it. Do some research along the way.
Use create-react-app to get up and running fast as well as boilerplate example projects on github to see how others have used it.
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Personally, I recommend React's official tutorial, to get started with. It is very well written, and will quickly get you up to speed with all the core parts of React.
The core concept behind React is really simple — your UI is a pure function of your data (state), go ahead with that in mind; and with the above aids, you will master it in no time. :)