Something like this:
HTML Code:
<script type="text/javascript">
function AddToList()
{
var theList = document.getElementById("the-list");
var newItem = document.getElementById("newItem".value;
// Now append the innerHTML
theList.innerHTML += "<li>"+newItem+"</li>";
}
</script>
<input type="text" id="newItem" size="30"/>
<input type="button" value="Add" onClick="AddToList();"/>
<p>
<ul id="the-list">
</ul>
Committing it to the database is a whole different story. Your best bet is to save each item into an array and then use AJAX to send it to a PHP page
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