How to create a category menu?

You have to register menu’s in your theme’s functions.php unless you only wish to use them in widgetised areas.

As an example:-

<?php register_nav_menu('main', 'Main Navigation Menu'); ?>

Then you have to call that menu into your template file where you wish it to be displayed, so for example, in the header (header.php):-

<?php wp_nav_menu( array('main' => 'Main Navigation Menu' )); ?>

Then you can construct the menu in the WordPress back office under ‘Appearance’ > ‘ Menu’s’ including necessary pages and categories as you wish.

You can set the menu to auto include top level pages as they are created as well.