Edit in JSFiddle

class Timer extends React.Component {

  constructor() {
    super();
    this.tick = this.tick.bind(this);
  	this.state = {
      secondsElapsed: 0,
      isStart: false
    };
  }

  tick() {
    this.setState({
      secondsElapsed: this.state.secondsElapsed + 1
    });
  }

  start() {
    if(!this.state.isStart) {
      this.interval = setInterval(this.tick, 1000);
      this.setState({
        isStart: true
      });
    }
  }

  stop() {
    if(this.state.isStart){
      clearInterval(this.interval);
      this.setState({
        isStart: false
      });
    }
  }

  reset() {
    clearInterval(this.interval);
    this.setState({
      secondsElapsed: 0,
      isStart: false,
    });
  }

  componentWillUnmount() {
    clearInterval(this.interval);
  }

  render() {
    return (
      <div>
        Seconds Elapsed: {this.state.secondsElapsed}
      <div>
          <button onClick={this.start.bind(this)}>start</button>
          <button onClick={this.stop.bind(this)}>stop</button>
          <button onClick={this.reset.bind(this)}>reset</button>
      </div>
            </div>
    );
  }
}

React.render(<Timer />, 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>