Edit in JSFiddle

var TimerExample = React.createClass({

    getInitialState: function(){

        // This is called before our render function. The object that is 
        // returned is assigned to this.state, so we can use it later.

        return { elapsed: 0 };
    },

    componentDidMount: function(){

        // componentDidMount is called by react when the component 
        // has been rendered on the page. We can set the interval here:

        this.timer = setInterval(this.tick, 50);
    },

    componentWillUnmount: function(){

        // This method is called immediately before the component is removed
        // from the page and destroyed. We can clear the interval here:

        clearInterval(this.timer);
    },

    tick: function(){

        // This function is called every 50 ms. It updates the 
        // elapsed counter. Calling setState causes the component to be re-rendered

        this.setState({elapsed: new Date() - this.props.start});
    },

    render: function() {
        
        var elapsed = Math.round(this.state.elapsed / 100);

        // This will give a number with one digit after the decimal dot (xx.x):
        var seconds = (elapsed / 10).toFixed(1);    

        // Although we return an entire <p> element, react will smartly update
        // only the changed parts, which contain the seconds variable.

        return <p>This example was started <b>{seconds} seconds</b> ago.</p>;
    }
});


ReactDOM.render(
    <TimerExample start={Date.now()} />,
    document.getElementById('container')
);

<script src="https://facebook.github.io/react/js/jsfiddle-integration-babel.js"></script>

<div id="container">
    <!-- This element's contents will be replaced with your component. -->
</div>

* {
    padding:0;
    margin:0;
}

html{
    font:14px normal Arial, sans-serif;
    color:#626771;
}

body{
    padding:60px;
    text-align: center;
}