How do I install Arma 2 and Arma 2: Operation Arrowhead on Steam?

Run Steam as Administrator (right-click on the Steam icon and click on "Run As Administrator").

Install Arma 2.

Run Arma 2 once.

Install Operation Arrowhead.

Run Operation Arrowhead through Steam (Battleye will now install automatically).

If you wish, you can also install the Arma 2: Operation Arrowhead beta (for the purposes of running Mods etc.). It will appear as a separate item in your Library.