The easiest way is to use refs which are a React function that will allow you to call methods on instances of components that you returned from render() .
You can read a little more about them in the documentation: https://facebook.imtqy.com/react/docs/more-about-refs.html
In this case, just add ref to your video tag as follows:
<video ref="vidRef" src="some.mp4" type="video/mp4"></video>
Thus, when you add click handlers to your buttons:
<button onClick={this.playVideo.bind(this)}>PLAY</button>
The playVideo method will have access to your video link through refs :
playVideo() { this.refs.vidRef.play(); }
Here is a working DEMO, so you can see a complete example.
source share