Before you start, make sure you have done the following:
Have Steam running as an Administrator
Have the Arma 2 and Arma 2 Operation Arrowhead installed.
If you did all of the above you should now download the DLC files from Steam library as you would with any other Steam game (go to your library, select the desired product and click "install"). After the download finishes, click "play" and the DLC should automatically install the remaining files necessary for you to play it. Alternatively, you can just start your Arma 2 Operation Arrowhead. It should detect the DLC files automatically and install them by itself before launching.
Please note that the Arma 2: Army of the Czech Republic DLC will not appear in your steam library as the other two DLCs do. Instead, it will be included in your Arma 2 Operation Arrowhead directly (you should still see the install window during your first time launch though).