First off, make sure you're at the correct webpage to listen to the radio station:
http://www.Live365.com/stations/record4/
Unfortunately you'll have to register if you are new to Live365, but it's pretty painless. They send out junk email, no more than one a month, and they've got a solid privacy policy.
To join, if you haven't already, look in the upper right hand corner for a link called Sign Up, or just go directly to this page: http://www.live365.com/members/login.live?action=none

Once you've signed up, logged on and have made it back to the station's page, click on this button:

If you unfortunately see this:
(it's a dimmed out)
the station is currently not broadcasting.
If it's dimmed go to http://listento.thedrunkidiots.com/ for some Drunk Idiots listening.

If you see the lit up Play button, click on it.
(Not the one on this page, but the one on the radio station's page...)

The radio player works in a pop-up window, so if you have pop-ups disabled on your computer, you need to re-enable them to listen to the station. You'll have to figure this one out. There's a lot of ways to block pop-ups, so you will have to figure that one out.
Once you get the pop up, the program will tell you that you need a media player to listen to the show. It'll ask you if you want to download the Live365 player. This isn't necessary if you already have a player like RealOne Player. The pop-up that comes up telling you that you need a player, should have a link towards the bottom that allows you to choose a different player. Then the program will take a quick look and see what media players you have available on your computer and let you choose which you want to use.
The program will offer a Live365 player for download, you don't need that. You can just use RealPlayer or Windows Media Player or even WinAmp, personally, I use Real and it works just fine.
Once you choose your player, the program starts setting everything up and it should start playing after a while. Once the player window is loaded, you may have to click on the blue play button on the player. I usually do this and stuff happens.

Still lost? No Worries.
If we're currently not doing a show we can try to help you when we're online:

One other source of information would be Live365.com's actual help page: http://help.live365.com/.
If even after all of that try emailling us and we'll see what we can do... webmaster@thedrunkidiots.com