You can't.
C# is a Server side language, it doesn't run on the client - so it has no direct access to client hardware, including the microphone.
To do this you need something that runs on the client and can access the hardware - which means you are pretty much going to need Flash (yeuch), Silverlight, or HTML5. And there is a good chance that this won't work well (if at all) across all platforms. But...
html5 audio recording - Google Search[
^] may help.