Customising WP theme Twenty Twelve

Do not edit the theme itself. First create a child theme for your changes. Or install a custom CSS plugin.

See also:

https://www.ads-software.com/support/topic/how-to-move-menu-below-header-image-in-twenty-twelve-theme?replies=40

Definitely use a child theme!

Which of those 2 options is the most straight-forward for me to work out how to do? I’m not especially technically savvy.

You actually need to use a child theme to do what you are asking about – because it involves modifying the header.php file. Custom CSS only covers CSS changes.