I think the error because the elements are undefined ,so you need to add window.onload
event which this event will defined your elements when the window is loaded.
window.addEventListener('load',Loaded,false);
function Loaded(){
var myButton = document.getElementById("myButton");
var myTextfield = document.getElementById("myTextfield");
function greetUser(userName) {
var greeting = "Hello " + userName + "!";
document.getElementsByTagName ("h2")[0].innerHTML = greeting;
}
myButton.onclick = function() {
var userName = myTextfield.value;
greetUser(userName);
return false;
}
}