Getting a static two-level menu?

Hello,
I think this is a general question so I post it here rather than in the themes section.
For a self-hosted site (probably using the Responsive theme as a building block and adding my amendments in a child theme, but possibly using some other theme) what is needed in order to get a static two-level sidebar menu/navigation as in the image attached? Static in the sense that both menu levels are visible and stay in place all the time. Do I need to re-write php-code (ouch, I don’t know PHP) or is it enough to re-write CCS hovering code?

Image does not appear to show up when I try to link it, but it is here: http://i.imgur.com/9hiY7z4.jpg