There are several ways to connect to the chat room, but the preferred way is by using an irc client. There are several clients for connecting to IRC, below is a list of a few reccomended ones.
Mac OS X
Connect to the server irc.furnet.org, and go to channel #wyvrncity by typing "/join #wyvrncity"
Or, if your client supports it, you can click this link: irc://irc.furnet.org/wyvrncity