My website has three components:
I understand how to implement the horizontal aspect of the liquid layout so that the nav remains fixed while the content area takes up remaining width, but I don't understand how to implement the vertical aspect of liquid layout so that both the nav and content area take up at least the remainder of the height and at most the height of their content (assuming that this is taller than the screen less the header height).
Possible with divs?
Yes, it's possible. Take a look at Ryan Fait's sticky footer, and my previous answer to a similar question.