Run both Arma II and ArmA II combined Operations once from your Steam games library to complete the installation of the base content.
Then follow this guide How to install DayZ (Steam version) - DayZ Wiki
to install the Day Z Mod. If you've already installed Day Z, go back, remove the Day Z hook from the launcher and run both games from Steam.
Unfortunately, it's not made crystal clear in most install guides so it's an easy mistake to make but luckily it's just as easy to fix. Welcome to alpha.