constructor(props) {
  super(props);
  this.state = {
    clicked: false
  };
}

render() {
  const { clicked } = this.state;
  const buttonStyle = clicked ? { backgroundColor: 'red' } : { backgroundColor: 'blue' };

  return (
    <button style={buttonStyle} onClick={this.handleClick}>Click Me</button>
  );
}

handleClick = () => {
  this.setState(prevState => ({
    clicked: !prevState.clicked
  }));
}