When working with React, a good approach is to start thinking about components from a User Experience point of view, start writing the most basic ones, and then write more complex one making use of thouse in order to build more complex UIs.
It is possible to use React in conjunction with pretty much any technology stack, as it doesn't make any assumption about this matter. It is even possible to integrate it, more or less painfully, into a Maven build.
If you take a look at both the React tutorial and at my playground, you'll notice that mine is a simplified one based upon the first. The tutorial is about building a comment list, along with a form which lets you add more comments, and it comes with a simple backend as well.
My playground, on the other hand, is a list of transactions, with a form which lets you add more transactions, therefore altering the balance of the account accordingly. No backend, just a small proof of concept for React.