There are a few approachs that I have come across, some I like, some I hate.
I've seen HTML5 and CSS3 approachs and I've seen jQuery approaches, I prefer the HTML5 route as it is more stable and one well written style sheet should do it, but it is not widely supported yet. Don't get me wrong, with a forward thinking client, you could be laughing, but you might have to create a second non HTML5 site for older browser.
jQuery, its not as cool as some of the dynamic resizing that can happen with the HTML5 route, but it is more stable across older browsers.
I keep thinking that an awesome HTML site and a jQuery mobile site is the best route, but that takes more time.
Have you looked into jQuery mobile yet?
The biggest problem we have encountered with our clients is selling it as an approach. Most of them just don't care! They don't see the point in spending the extra money and often prefer the idea of a site that looks the same across the board, I realise it is my job to sell it to them, but we all know how it is.
Our contract is current and previous 2 browsers, so we have agreed that we aren't going to really start working towards fully responsive until the browser math is in our favour.