How to display my categories in a list (to a post, not the sidebar)?

Using wp_list_categories

http://codex.wordpress.org/Template_Tags/wp_list_categories

Something like this should give you what you want

$args = array(
    'hierarchical' => true,
    'hide_empty' => 0,
    'title_li' => ''
    );

wp_list_categories($args);