I've worked with jQuery, script.aculo.us, and mootools, and I would highly recommend jQuery, which seems to trump a lot of the other frameworks in its ease of use.
For someone who is familiar with HTML and CSS, jQuery fits the paradigm really well, and makes the transition into Javascript very simple.
For example, with html such as this:
<div id="content">
<h2>Heading</h2>
<p class="featured">This content</p>
</div>
You might have CSS selectors that looked like this:
#content {
margin: 0 auto;
width: 760px;
}
#content h2 {
font-size: 110%;
}
#content p.featured {
font-weight: bold;
}
In jQuery, you can manipulate those elements using the same selectors:
$('#content').hide();
$('#content h2').html('New Heading');
$('#content p.featured').css('border', '#cccccc 1px solid');
jQuery also has excellent documentation that can really help a beginner jump right in.