Step 1: Install WoW
Step 2: Choose your server
Click on the link to it. Register a new account on the server site you wish to play on. (This will be your World of Warcraft login) After making an account, find "Connecting to server" or instructions on how to connect. To play on a private server, they should give you a IP address, or website. This will be typed in one of your World of Warcraft files. OK here is where it gets a little harder. Go to your World of Warcraft folder. (Default: C:\Program Files\World of Warcraft) and locate "realmlist.wtf" open this with notepad, or another text editor. It should say set realmlist us.worldofwarcraft.com, delete that so it says set realmlist "your server". For our case "set realmlist 126.96.36.199" save the file and exit.
Step 3: Play!
FYI: I no longer play World of Warcraft. WOTLK was too scary for me. :[