How do I change the default wordpress navigation header that comes with my theme?

Assuming the theme is using wp_nav_menu You should be able to find where the menu is being pulled in (most likely your header).

The line you are looking for is going to look something like this
<?php wp_nav_menu( array('menu' => 'Project Nav' )); ?>

Once you find it create a child theme then either remove the current menu and create your own or move it to the location you would like.

You may also be able to just style it was CSS.

Because most themes integrate the menu in different ways there is no way to provide instructions without knowing the theme you are using.