I wouldn't walk the PlayOnLinux route myself. Often you have the game already installed on a Windows partition or you used the vanilla Torrent which makes using plain Wine much easier. Running the game this way you won't hardly see the difference between running it under Linux/Ubuntu and Windows.
In the case of Ubuntu the steps would be roughly these:
Install Wine: `sudo apt-get install wine`
After the install is finished run `winecfg` as a local user (so no sudo). The only thing I do here is go to the 'Drives' tab and click the 'autodetect' button, throw away everything accept for the 'drive_c' and '/home/<username>' entries and click the 'OK' button. This will setup everything wine will need to run so don't skip this.
Unpack or copy your vanilla wow install somewhere, I like to create a '~/Games' folder where I store my games.
Once all files are in place navigate to that folder and open `WTF/Config.wtf` in your favorite text editor and add the line ' SET gxApi "opengl" ', this switches the game to using OpenGL for rendering which Wine supports directly and not DirectX which is emulated by Wine by using OpenGL. Alternatively you can use my Config.wtf attached to this post, note that my file has been tweaked out to get all possible effects out of the game possible, if you have a halfway decent GFX card it should be able to handle this just fine. You probably want to change the resolution though if it's something else than 1920x1080, search for 'gxResolution'.
That's it! Run the game: `wine Wow.exe` You'll have to be standing in the game folder to run that or else you have to prefix it with the path.
That's all you need really and it will run fine. If you'd like you can also create a (gnome) menu icon: https://help.ubuntu.com/community/WorldofWarcraft#Gnome_menu_icon
For more details: https://help.ubuntu.com/community/WorldofWarcraft
Download Config.WTF
Hope this is helpful!