How do I browse a website that uses WebGL?

Actually it says there you need a Browser that supports WebGL, not openGl. As you can see in the following links, no officially released version of Firefox, Chrome or Opera support WebGL at 100%. The nightly builds do but they still need work:

http://www.khronos.org/webgl/wiki/Getting_a_WebGL_Implementation

http://wakaba.c3.cx/w/webgl.html

http://en.wikipedia.org/wiki/WebGL

As WebGL uses Canvas then it needs a browser that supports HTML 5 (Which is like the latest for browsers)

Also there is a web page to test if your browser supports WebGL: http://www.doesmybrowsersupportwebgl.com/

Remember that apart from the Browser supporting WebGL, you need a video card that supports OpenGL ES 2.0 which would be supported if your graphics card supports OpenGL 2.0+.

UPDATE
With Firefox 4.x and starting with Chrome 9 you have support for WebGL apps. For course, for the time being, Chrome renders faster than Firefox but Firefox is more standard than Chrome.