Category based navigation menu

Hi,
I’ve been searching for some guidance on this subject but to no avail.
I want to have an horizontal menu that displays all my parent categories, and when I click on one of those, below it displays another horizontal menu but with the child categories of the clicked one.
The styling I think I can handle, but the php that would display the correct children upon clicking on the parent is what I cannot get right.

I’ve found that this kind of menu is very used but with pages instead of categories. This is a code I found and I replaced every ‘pages’ for ‘categories’, but it didn’t work (it was worth trying…).

<ul id="nav">
     <?php wp_list_categories('depth=1&title_li='); ?>
</ul>
<?php if(wp_list_categories("child_of=".$post->ID."&echo=0")) { ?>
     <ul id="nav-sub">
          <?php wp_list_categories("title_li=0&child_of=".$post->ID."&sort_column=menu_order");?>
     </ul>
<?php } ?>

Any help will be appreciated.
Thank you very much for your time!

Martín.