To enable this, you have to go login again. There is no special URL or anything to go to... the load balancer will automatically hand your request off to the dedicated server.
If anybody feels like faking their cookie to get free access to the paid user server, you have a day or so to enjoy it before I fix the LJ code and make that impossible. Currently the load balancer checks for the presence of a cookie that the login page sets, but the paid server never validates you're actually a paid user. I'm aware of the problem ... it'll get fixed when I have free time.
Update: Don't thank me... I did all the easy work. Dormando did the ugly stuff. :-)
Update 2: This isn't the cool secret project I've been talking about lately. This was a 20 minute hack. The cool secret project is much cooler than this. :-)