Adding HTML elements with JavaScript

node = document.getElementById('YourID');
node.insertAdjacentHTML('afterend', '<div>Sample Div</div>');

Available Options

beforebegin, afterbegin, beforeend, afterend

As you didn't mention any use of javascript libraries (like jquery, dojo), here's something Pure javascript.

var txt = document.createTextNode(" This text was added to the DIV.");
var parent = document.getElementById('div');
parent.insertBefore(txt, parent.lastChild);

or

var link = document.createElement('a');
link.setAttribute('href', 'mypage.htm');
var parent = document.getElementById('div');
parent.insertAfter(link, parent.firstChild);

Instead of dealing with the <div>'s children, like other answers, if you know you always want to insert after the <a> element, give it an ID, and then you can insert relative to its siblings:

<div id="div">
  <a id="div_link">Link</a>

  <span>text</span>
</div>

And then insert your new element directly after that element:

var el = document.createElement(element_type); // where element_type is the tag name you want to insert
// ... set element properties as necessary

var div = document.getElementById('div');
var div_link = document.getElementById('div_link');
var next_sib = div_link.nextSibling;

if (next_sib)
{
  // if the div_link has another element following it within the link, insert
  // before that following element
  div.insertBefore(el, next_sib);
}
else
{
  // otherwise, the link is the last element in your div,
  // so just append to the end of the div
  div.appendChild(el);
}

This will allow you to always guarantee your new element follows the link.