Add a list item through javascript

If you want to create a li element for each input/name, then you have to create it, with document.createElement ^[MDN].

Give the list the ID:

<ol id="demo"></ol>

and get a reference to it:

var list = document.getElementById('demo');

In your event handler, create a new list element with the input value as content and append to the list with Node.appendChild ^[MDN]:

var firstname = document.getElementById('firstname').value;
var entry = document.createElement('li');
entry.appendChild(document.createTextNode(firstname));
list.appendChild(entry);

DEMO

Try something like this:

var node=document.createElement("LI");
var textnode=document.createTextNode(firstname);
node.appendChild(textnode);
document.getElementById("demo").appendChild(node);

Fiddle: http://jsfiddle.net/FlameTrap/3jDZd/