how to change WordPress menu markup/classes

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Changing the CSS is the simplest way to apply your desired styles.

Another alternative, as Jack mentioned, is to create a custom walker. The Codex has a good overview.

The third option is a happy medium – you can customize the menu partially just with your wp_nav_menu() call. For example, this call

wp_nav_menu(array(
    'menu' => 'myMenu', // change this to call your desired menu
    'container_class' => 'topNav', // changes outer <div> class
    'items_wrap' => '<ul>%1$s</ul>' // strips id & class from <ul>
));

will give you this output:

<div class="topNav">
   <ul>
      <li id="menu-item-89" class="some random wordpress classes">
         <a href="#">about</a>
         <ul class="sub-menu">
            <li id="menu-item-90" class="some random wordpress classes"><a 
               href="http://test">example</a></li>
         </ul>
      </li>
      <li id="menu-item-92" class="some random wordpress classes"><a 
         href="http://2">example</a></li>
   </ul>
</div>

so there’s less CSS to change, but you also don’t have to build an entire Walker.