I just received a new client account for a radio station in my area. And really need some help. They want to be able to have their broadcast played through the site live. How is the best/easiest/cheapest way to do this? I think that they will need to broadcast over a digital feed in order to play it on the internet. If anyone knows how to do this or where I can find some useful info about it, that would be really great.

The site they gave me as an example is www.670thescore.com. What I need to do is on the left side of the screen under listen live.

You'll need a streaming solution.

LNR is correct.

I know that the part from the radio to the net is not that difficult.
A radio hooked in front of a shoutcast server can do it easily.
I've worked on a web agency who provided this service for an associative radio for years, and it was nothing more than this:

radio --> line input on a sound card on the server --> munched through a shoutcast (or maybe iceCast) mp3 server --> To the world

The problem might be the bandwith, as each people listening to a feed will consume a constant bandwith.

Or you can look for resource like Rivendell's radio streaming software.
http://www.rivendellaudio.org/

Rivendell is a complete radio broadcast automation solution, with facilities for the acquisition, management, scheduling and playout of audio content. It has all of the features one would expect in a modern, fully-fledged radio automation system, including support for both PCM and MPEG audio encoding, full voicetracking and log customization as well as support for a wide variety of third party software and hardware.

After that, the only thing to take care, is the bandwith...