How can I allow a client to edit certain parts of a static site?

in first you have to know how convert your static html pages into wordpress themes ,
then about your navbar put this code in your theme function.php

function register_my_menu() {  register_nav_menu('header-menu',__( 'Header Menu' ));}add_action( 'init', 'register_my_menu' );

then go to your header.php where your navbar is and remove nav and put this code in it

<?php wp_nav_menu( array( 'theme_location' => 'header-menu' ) ); ?>

and it will put your custom navbar from wordpress dynamic . for instructions look at wordpress navbar