It really should be built from the ground up with CSS Media Queries in mind to begin with. That will generally give you better results than trying to cobble the various css together for each new screen size after it has already been built. That's not saying you can't do it, you just may find it would have been easier to start from scratch.
Here's a good "jump off point" regarding media queries...
Responsive web design isn't icing that you slap on after everything else is cooked. Rather it's a fundamental ingredient. If you want a truly adaptive layout, you'll need to rebuild with style sheets designed for each target device, (mobile, tablet, desktop -- portrait & landscape).
If you're looking for a quick fix, you might try % widths on your containers. However this can produce some ugly side effects.
Liquid layout with side effects:
Semi-Liquid Layout with min- and max-widths in px: