Firstly, I would recommend that you make your changes in a Child Theme. It's the only recommended way of modifying a WordPress theme and takes about five minutes to do.
Once you have a minimal child theme activated, you can copy your parent theme's header.php file into your child theme's directory and WordPress will automatically use it in preference to the version in the parent theme's directory.
Regardless of whether you have a child theme or not, you need to access the header.php code from the Dashboard (Appearance --> Editor).
Once in the code editor, you need to delete all the code above except for the following lines:
<div id="top-image">
<div id="top-image-wrap">
<img src="<?php echo get_template_directory_uri(); ?>/img/top-image-1.jpg" />
</div>
</div>
You may not actually need both those divs, but hey, let's not tempt fate, eh?
:)
This also demonstrates one of the advantages of using a child theme. You are only altering the child theme's version of the file. The parent theme's version remains unaltered. So you can always get back to square one, either by copying the parent theme's version back over the child theme version, or by reactivating the parent theme.
Then you need to edit the src attribute to point to the image you want to use. Let's suppose you've created a child theme. The easiest thing to do would be to create a new directory in your child theme's folder (let's call it 'images') and copy your header image into it. Let's assume you've called the image "logo.jpeg".
Now you can reference the image as follows:
<img src="<?php bloginfo('stylesheet_directory'); ?>/images/logo.jpeg" />
When you have your image showing on your page, we may need to do some tidying up of its size and position, but let's get it showing first!
Good luck.
Cheers
PAE