React.js how to pass callbacks to child components?

You are passing this.onUserInput as a property to FirstNestedComponent. Therefore, you should access it in FirstNestedComponent as this.props.onUserInput.

var FirstNestedComponent = React.createClass({
    render: function() {
        return (
            <div>
                <SecondNestedComponent
                    onUserInput={this.props.onUserInput}
                />
            </div>
        );
    }
});