How to set focus on an input field after rendering?

@Dhiraj's answer is correct, and for convenience you can use the autoFocus prop to have an input automatically focus when mounted:

<input autoFocus name=...

Note that in jsx it's autoFocus (capital F) unlike plain old html which is case-insensitive.

You should do it in componentDidMount and refs callback instead. Something like this

componentDidMount(){
   this.nameInput.focus(); 
}

class App extends React.Component{
  componentDidMount(){
    this.nameInput.focus();
  }
  render() {
    return(
      <div>
        <input 
          defaultValue="Won't focus" 
        />
        <input 
          ref={(input) => { this.nameInput = input; }} 
          defaultValue="will focus"
        />
      </div>
    );
  }
}
    
ReactDOM.render(<App />, document.getElementById('app'));

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.3.1/react.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react/15.3.1/react-dom.js"></script>
<div id="app"></div>

Focus on mount

If you just want to focus an element when it mounts (initially renders) a simple use of the autoFocus attribute will do.

<input type="text" autoFocus />

Dynamic focus

to control focus dynamically use a general function to hide implementation details from your components.

React 16.8 + Functional component - useFocus hook

const FocusDemo = () => {

    const [inputRef, setInputFocus] = useFocus()

    return (
        <> 
            <button onClick={setInputFocus} >
               Focus
            </button>
            <input ref={inputRef} />
        </>
    )
    
}

const useFocus = () => {
    const htmlElRef = useRef(null)
    const setFocus = () => {htmlElRef.current &&  htmlElRef.current.focus()}

    return [ htmlElRef, setFocus ] 
}

Full Demo

React 16.3 + Class Components - utilizeFocus

class App extends Component {
  constructor(props){
    super(props)
    this.inputFocus = utilizeFocus()
  }

  render(){
    return (
      <> 
          <button onClick={this.inputFocus.setFocus}>
             Focus
          </button>
          <input ref={this.inputFocus.ref}/>
      </>
    )
  } 
}

const utilizeFocus = () => {
    const ref = React.createRef()
    const setFocus = () => {ref.current &&  ref.current.focus()}

    return {setFocus, ref} 
}

Full Demo