A real Hello World example for react

I got frustrated following the React "Hello, World" and tutorial because of the implied magic. How does it actually work? Where does it fit into a html page? How do I run React locally?

The "Hello, World" has a 4 line example that does not actually work: this is the minimal react "Hello, World". If you save this to a file (e.g. hello_world.html), you will be able to open it with your favorite web browser:

<!DOCTYPE html>
                <meta charset="UTF-8" />
                <script src="https://unpkg.com/react@latest/dist/react.js"></script>
                <script src="https://unpkg.com/react-dom@latest/dist/react-dom.js"></script>
                <script src="https://unpkg.com/babel-standalone@latest/babel.min.js"></script>
                <script type="text/babel">
                                <h1>Hello, World!</h1>,
                <div id="root"/>

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