The best way to learn a new technology is building some real world stuff with it. That's how I learned React while getting started 2 years back. If I were to start all over again, I would repeat the same process. Here is how my learning path would look like :
The official getting started guide and React tutorial are very good starting points. I would read them completely.
After implementing the simple comment system (from the official tutorial above) I would build a small project with React - may be some simple app that I built using a different framework. This will help me apply what I learned into a real world scenario. Plus it can also help me identify my weaknesses.
Learn how to test React components because testing is important.
For bigger projects some kind of architecture will really help me. So, I will dive into Flux and understand all the concepts.
I would redo a slightly bigger project (that I did in a different tech) in React and Flux.
Learn Redux and compare it with Flux. Redo the above using Redux.
While doing all these, one would be seeing ES6 code, gulp, babel, webpack everywhere. So, I would make myself comfortable with front-end tooling and all of the above.
The last part would be reading a lot of code written by others and taking up a real world project (and eventually push it to production).