Creating a nav menu

First, be sure your theme supports wp_nav_menu which is goes into a template file – such as header.php – with the template tag function

<?php wp_nav_menu( $args ); ?>

which also requires a function in functions.php. See http://codex.wordpress.org/Function_Reference/wp_nav_menu

That will initiate the WordPress 3 menu system that will appear in Dashboard>>Appearance>>Menus

Next, read http://codex.wordpress.org/WordPress_Menu_User_Guide on how to make a menu with custom links that point to each category permalink, i.e. yourdomain.com/category/mycategoryname

Form the page structure with parent/child pages first, and then make the menu to follow your page structure.