What technologies are used to power Quake Live?
Specifically, how do you create a web application that makes such extensive use of 3D in the browser? The service requires you to download and install a plug-in in order to play. How do you create such a plug-in, and how does it interact with the web site?
Browser programs are very simply, programs. They are given an interface to interact with the browser, but beyond that, they can do anything a normal native application can do, like use DirectX or OpenGL.
Internet Explorer registers plugins using ActiveX. Firefox, Chrome, Safari and most other browsers use Netscape's NSPlugin API.
The MDC has plenty of documentation on writing plugins for Firefox. There is also a question on SO about writing plugins for IE.