Styling single posts depending on category

I should be able to do this by now, but I still find template tags tricky sometimes.

I have a subcategory ‘Scrapbook’, styled to have its children categories listed as links which open in a new window. I want these Scrapbook subcategories to differ greatly in style from the rest of the site, and for the single posts to display totally differently from those I have currently set up to display.

What’s the best way of doing this? I know it requires a conditional tag of some sort, in one of the template files… I have searched the Codex but not quite hit on the solution.

Thanks for any help…