How to do the simplest possible frontend ajax call from a plugin?

From codex: wp_ajax_{$action} and wp_ajax_nopriv{$action}
the dinamic part {$action} must be the same name as the function, so instead of:

add_action( 'wp_ajax_the_ajax_hook', 'the_action_function' );
add_action( 'wp_ajax_nopriv_the_ajax_hook', 'the_action_function' );

do:

add_action( 'wp_ajax_the_action_function', 'the_action_function' );
add_action( 'wp_ajax_nopriv_the_action_function', 'the_action_function' );