Hello,
You copy and paste your "Allods Online EN" folder to your new HDD (on your new computer). Then you download the launcher on your new computer from here :
http://allods.my.com/en/download
Once installed, you open the launcher settings (the little gear above your login name), and in the "Games and Download" tab, you indicate where is your "Allods Online EN" folder.
By default, you'll find your "Allods Online EN" folder here : C:\MyGames\
You only have the Allods client on your computer and some of your ingame personnal settings. Your character's progression is saved on Allods Online servers.