If you look at the Tabs Demo Page you can click on the Themig tab to view which styles are in use, currently it looks like this:
<div class="ui-tabs ui-widget ui-widget-content ui-corner-all" id="tabs">
<ul class="ui-tabs-nav ui-helper-reset ui-helper-clearfix ui-widget-header ui-corner-all">
<li class="ui-state-default ui-corner-top ui-tabs-selected ui-state-active"><a href="#tabs-1">Nunc tincidunt</a></li>
<li class="ui-state-default ui-corner-top"><a href="#tabs-2">Proin dolor</a></li>
<div class="ui-tabs-panel ui-widget-content ui-corner-bottom" id="tabs-1">
<p>Tab one content goes here.</p>
</div>
...
</div>
Then you can use the jQuery UI CSS Framework documentation to find a description of each general class. The widget specific classes aren't listed, as they're well...per-widget.
The best way to get an idea of what those classes do is to use ThemeRoller, or look at the default theme (for example here) and just look at the CSS for those classes, you can use just that and adjust for your own needs, here's the current base theme CSS for .ui-tabs-*
classes:
.ui-tabs { position: relative; padding: .2em; zoom: 1; }
.ui-tabs .ui-tabs-nav { margin: 0; padding: .2em .2em 0; }
.ui-tabs .ui-tabs-nav li { list-style: none; float: left; position: relative; top: 1px; margin: 0 .2em 1px 0; border-bottom: 0 !important; padding: 0; white-space: nowrap; }
.ui-tabs .ui-tabs-nav li a { float: left; padding: .5em 1em; text-decoration: none; }
.ui-tabs .ui-tabs-nav li.ui-tabs-selected { margin-bottom: 0; padding-bottom: 1px; }
.ui-tabs .ui-tabs-nav li.ui-tabs-selected a, .ui-tabs .ui-tabs-nav li.ui-state-disabled a, .ui-tabs .ui-tabs-nav li.ui-state-processing a { cursor: text; }
.ui-tabs .ui-tabs-nav li a, .ui-tabs.ui-tabs-collapsible .ui-tabs-nav li.ui-tabs-selected a { cursor: pointer; }
.ui-tabs .ui-tabs-panel { display: block; border-width: 0; padding: 1em 1.4em; background: none; }
.ui-tabs .ui-tabs-hide { display: none !important; }