I don't believe there is HTML support for audio capture. There is a working group that produced http://www.w3.org/TR/xhtml+voice/ but I don't believe this is implemented in any browser except Opera (see http://dev.opera.com/articles/voice/).
You could look at the WAMI toolkit. WAMI toolkit is an interesting project from MIT - http://wami.csail.mit.edu/. In their own words "WAMI: Web-Accessible Multimodal Applications. WAMI is a simple way to add speech recognition capabilities to any web page." WAMI gives you a java applet that can run in your web page to perform audio capture for speech recognition. In their examples, the recognition is performed on the server.
I suspect one could use Flash, ActiveX or Java within the browser and run local speech recognition from within your web page. However, you would need to install a recognition engine (or verify that one is available).