recording from bbc iplayer

I am new to audacity, and am having trouble discovering how to record from radio being streamed via MS IE9.

So far I have succeeded recording the radio stream but it is picking up noises via the microphone (example: shutting the room door during a recording is clearly picked up). Muting the microphone stops audacity picking up any sound, so audacity must be just using the built in microphone to record from the PC speakers.

Can someone kindly point in the right direction please?

My naive thoughts are that the PC has several possible sources of audio - CD player; line-in; BBC I-player; microphone etc - Do these all connect into a common channel or bus?

How do I select one or more of these channels into audacity? Is this done in audacity or in Windows & how?
How to mute the microphone without muting all sound into audacity?

To begin with I would just like to record to audacity only from the BBC Iplayer radio, but also play the sound through the PCspeakers.

Running a Dell XPS17 (laptop); Windows 7 64bit home premium; ControlPanel/sound indicates the sound system is ?Realtek but I do not know whether that is relevant.

Feeling utterly confused, so any and all help much appreciated.

TIA

What you are wanting to do is what the Audacity manual refers to as “Recording Sounds that are playing on your computer”.
See here: http://manual.audacityteam.org/man/FAQ:Recording#streaming