Add Text & Call to Action Button to Homepage Featured image

How do I add text and a call to action button to the featured image set for my static homepage?

This suggestion was made but I don’t know how to go about accomplishing this code:
To add a call to action text & button, you will probably have to create a child theme & add code to a copy of the header.php.

Any assistance or feedback is greatly appreciated. Thank you.

The page I need help with: [log in to see the link]