Twenty Twelve customization sidebar

I want to add a background color to the header of my Twenty Twelve theme.

I looked at the Preview screen and found a robust list of ways to modify the theme, one of which is the color of the background of the header.

When I looked at my installed theme, the Customize options are really pathetic and aren’t nearly as numerous as in the preview.

How do I gain access in my installed theme to the capabilities in the preview theme? All I want to do is add a simple solid color to the background of the header.