You'll need to keep the current value of the input in state (or pass changes in its value up to a parent via a callback function, or sideways, or <your app's state management solution here> such that it eventually gets passed back into your component as a prop) so you can derive the disabled prop for the button.
Example using state:
<meta charset="UTF-8">_x000D_
<script src="https://fb.me/react-0.13.3.js"></script>_x000D_
<script src="https://fb.me/JSXTransformer-0.13.3.js"></script>_x000D_
<div id="app"></div>_x000D_
<script type="text/jsx;harmony=true">void function() { "use strict";_x000D_
_x000D_
var App = React.createClass({_x000D_
getInitialState() {_x000D_
return {email: ''}_x000D_
},_x000D_
handleChange(e) {_x000D_
this.setState({email: e.target.value})_x000D_
},_x000D_
render() {_x000D_
return <div>_x000D_
<input name="email" value={this.state.email} onChange={this.handleChange}/>_x000D_
<button type="button" disabled={!this.state.email}>Button</button>_x000D_
</div>_x000D_
}_x000D_
})_x000D_
_x000D_
React.render(<App/>, document.getElementById('app'))_x000D_
_x000D_
}()</script>
_x000D_