Here's a simple script:
<div id="'hello'">Hello World. </div>
<script type="'text/javascript'">
var test=document.getElementById('hello');
test.appendChild(document.createTextNode('Goodbye World'));
</script>
This is your basic example of DOM manipulation. You create a variable and start manipulating the document based on that element. But here's something I bet you didn't know. That first line is not needed:
<div id="'hello2'">Hello World. </div>
<script type="'text/javascript'">
hello2.appendChild(document.createTextNode('Goodbye World'));
</script>
Anytime you create an element with an ID a variable with the same name is automatically available for you to use.
(Update: After some explorations it turns out that although this does sometimes work it's unreliable in strict mode. It's probably not recommended for general use)