jQuery has a great selection of DOM traversing functions.
Lets say that for instance, you start with
<html>
<body>
<table id="aTable"></table>
</body>
</html>
You can then use jQuery to add to the table:
<html>
<head>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js" />
<script type="text/javascript">
$(document).ready(function(){
$("#aTable > tbody").append('<tr id="row1"><td>some data</td></tr>');
});
</script>
</head>
<body>
<table id="aTable"></table>
</body>
</html>
This would add a single cell to the table. Note the tbody tag, I have found that this is needed as tbody is an implicit tag when rendered by browsers.
Now Let's go backwards. If you start with the cell already in the table, you can remove it very easily with the remove() function:
<html>
<head>
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4.2/jquery.min.js" />
<script type="text/javascript">
$(document).ready(function(){
$("#row1").remove();
});
</script>
</head>
<body>
<table id="aTable">
<tr id="row1">
<td>some data</td>
</tr>
</table>
</body>
</html>
And poof, it's gone. The good part about doing it this way is that you can use event handlers and all sorts of cool things to do all of this in an interactive way. There's no way that I can even scratch the surface of jQuery because I too am fairly new to it, but the docs are pretty good. Check it out
EDIT: this also assumes that you know what you'll be adding. If you need to do it on the fly, a little AJAX will go a long way (jQuery abstracts this to make it nice as well).