1. Theme tells that it has sidebar(s) using either register_sidebars(n) or one to several calls to register_sidebar(...). This is done in functions.php.
2. Where the sidebar should appear, you call dynamic_sidebar(), and if it returns false, you render some static stuff instead of widgets.

All this is explained in excruciating detail in WordPress documentation, so look it up in there, if you want to know exactly how it’s done. Now when all this is done, your call to dynamic_sidebar() (done inside <ul> and </ul> tags) will output the widgets selected to this sidebar in the following manner:

<li id="..." class="..."><h2 class="widgettitle">Pages</h2>
<ul>
<li><a href="...">Page 1</a></li>
<li><a href="...">Page 2</a></li>
</ul>
</li><li id="..." class="..."><h2 class="widgettitle">AnotherWidget</h2>
<ul>
<li><a href="...">Link 1</a></li>
<li><a href="...">Link 2</a></li>
</ul>
</li>

Now any Google-aware reader will already know, that horizontal menus can be made from unordered lists using the following CSS definitions:

#menu ul {
  list-style: none;
  margin: 0;
  padding: 0;
}

#menu li {
  float: left;
}

Now because the ul element doesn’t have margins or borders, and li elements float after each other, we could even have several unordered lists after each other, and still the result would look like one horizontal menu. Now the problem is how to get rid of the Widget names completely. Well, this can be done quite easily. If you look up the register_sidebar() function call from the Widgets API, you see that you can actually have an array of parameters governing the way widgets and their titles are outputted to the sidebar.

By setting before_widget and after_widget to empty strings, and not having <ul> and </ul> around
your call to dynamic_sidebar(), and setting before_title and after_title to beginning and end of a comment block, we achieve everything needed. So in your functions.php, you would have the following code (notice how I have named the sidebar “Topmenu” to make it easier to recognize that particular sidebar in WordPress widget configuration):

register_sidebar(array('name' => 'Topmenu',
		'before_widget' => '', 'after_widget' => '',
		'before_title' => '<!--', 'after_title' => '-->'));

Which would reduce the widget code shown above to something like this:

<!-- Pages -->
<ul>
<li><a href="...">Page 1</a></li>
<li><a href="...">Page 2</a></li>
</ul>
<!-- AnotherWidget -->
<ul>
<li><a href="...">Link 1</a></li>
<li><a href="...">Link 2</a></li>
</ul>

Now only thing you need to do is to put your menu-generating piece of code where you want it, in my case it was the header.php of my theme:

<?php /* Widgetized sidebar, if you have the plugin installed. */
if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar('Topmenu') ) : ?>
<ul>
<li><a href="http://www.somesite.com">Static menu item 1</a></li>
<li><a href="http://myblog.com">Static menu item 2</a></li>
</ul>
<?php endif; ?>

Now all you need is to go into WordPress site admin, and select Presentation > Widgets, and add the relevant widgets to your brand-new Topmenu (I use the Pages and Categories widgets). And you’re done!

Please leave comments if you have any questions or further suggestions.