onClick doesn't render new react component.

You probably want to have a stateful component that shows the other component next to the button after it was clicked. All you need to do is track whether the button was clicked:

class MyComponent extends React.Component {
  constructor(props) {
    super(props);
    this.state = {
      showComponent: false,
    };
    this._onButtonClick = this._onButtonClick.bind(this);
  }

  _onButtonClick() {
    this.setState({
      showComponent: true,
    });
  }

  render() {
    return (
      <div>
        <Button onClick={this._onButtonClick}>Button</Button>
        {this.state.showComponent ?
           <NewComponent /> :
           null
        }
      </div>
    );
  }
}

Here's a CodePen to show it in action.

HTML

<div id="root">loading...</div>

JSX

class NewComponent extends React.Component {
  render() {
    return (
      <div {...this.props}>
        new component
      </div>
    );
  }  
}

class Button extends React.Component {
  render() {
    return (
      <button {...this.props}>
        click
      </button>
    );
  }  
}

class App extends React.Component {
  constructor() {
    super();

    this.state = {
      clicked: false
    };

    this.handleClick = this.handleClick.bind(this);
  }

  handleClick() {
    this.setState({
      clicked: true
    });
  }

  render() {
    return (
      <div>
        <Button onClick={this.handleClick} />
        {this.state.clicked ? <NewComponent /> : null}
      </div>
    );
  }
};

React.render(
  <App />,
  document.getElementById("root")
);

Use instead: {this.state.clicked && <NewComponent />}