You will need a specialised socket application on the server-side to take the connections and do something with them; it is not something you would normally be doing from a web server's scripting interface. However it is a relatively simple protocol; my noddy Python SocketServer-based endpoint was only a couple of pages of code.
In any case, it doesn't really exist, yet. Neither the JavaScript-side spec nor the network transport spec are nailed down, and no browsers support it.
You can, however, use Flash where available to provide your script with a fallback until WebSocket is widely available. Gimite's web-socket-js is one free example of such. However you are subject to the same limitations as Flash Sockets then, namely that your server has to be able to spit out a cross-domain policy on request to the socket port, and you will often have difficulties with proxies/firewalls. (Flash sockets are made directly; for someone without direct public IP access who can only get out of the network through an HTTP proxy, they won't work.)
Unless you really need low-latency two-way communication, you are better off sticking with XMLHttpRequest for now.
I think it is important to mention, now that this question is over 1 year old, that Socket.IO has since come out and seems to be the primary way to work with sockets in the browser now; it is also compatible with Node.js as far as I know.