A unique serial key needs to be registered for your copy of ArmA 2 in order to play online. You can find your key in your My Account section, after clicking the game. That's the entire three-lines-long block of text.
Copy that key and launch the Arma Serial Key Changer application, found under the Start Menu, by right-clicking it and selecting "Run as Administrator". Use your key in this application.
Please note that if you do not use the "Run as Admin" option, and you have User Account Control enabled (it's on by default), the application may not work properly. This requirement does not apply to Windows XP, which does not use User Account Control.