The Thesis framework uses a unique system to customize while inheriting the parent theme’s functions and styles, different from the typical WordPress method of child/parent themes. You don’t actually build a separate theme folder with Thesis – you edit the files within /wp-content/themes/thesis/custom/ (or if it doesn’t exist yet, change the name of the “custom-sample” folder to “custom” and then edit the contents).
There are two basic files to start with – custom_functions.php and custom.css. Place any code you would normally place in the functions.php file of a child theme into custom_functions.php, and place any CSS you would normally place in the style.css of a child theme into custom.css.
Thesis reads these two files and automatically injects them like a child theme when rendering. There’s an images folder inside of /custom you can use for your graphics, too.
The great thing about this system of customizing Thesis is that it’s completely self-contained – you can copy your /custom folder to any other site running thesis, and your customizations also won’t be overwritten by updates to the Thesis theme itself.