What would be the common mistake of function being called every time the component renders?

You need to make sure that function is not being called while passing the function as a parameter.

render() {
  // Wrong way: handleClick is called instead of passed as a reference!
  return <button onClick={this.handleClick()}>Click Me</button>
}

Instead, pass the function itself without parenthesis:

render() {
  // Correct way: handleClick is passed as a reference!
  return <button onClick={this.handleClick}>Click Me</button>
}