Hello, and welcome to the forums. There are a few steps that you will need to follow in order to get your game working with the latest version of DCS World.
1. Open Steam and navigate to the games library tab.
2. Right click on A-10C and select the item labeled 'view CD key' (Copy that key down somewhere, you will need it.).
3. Follow each of the links below (two of them), and download everything on those pages.
http://www.digitalcombatsimulator.com/index.php?ProductId=21&end_pos=137&scr=product&lang=en
http://www.digitalcombatsimulator.com/index.php?scr=product&ProductId=8&end_pos=136&lang=en
4. After the downloads are completed, install DCS world FIRST.
5. When the World installation completes, you may install the A-10C module that you just downloaded from the Eagle Dynamics website. (Make sure you install the A-10C module after the world install is finished.).
6. Start up world, and launch any quick mission. It will ask you for your A-10C CD key that you copied down earlier.
**Note**: Do not use Steam to install any part of this package. The Steam version is out of date, and not in any way, shape, or form compatible with the current release. Uninstall the Steam version of A-10C and forget about it, only using it as a reference to your CD key for future re-installations of DCS World.
You will also need to create an account at http://Digitalcombatsimulator.com/ if you wish to play online. This is the same account that you will use for connecting to the master server.