Q: How do I retrieve an app that I bought.  The icon is in my library.  But the program isn't in my device. When I look in the file that contain the app and try to open it,  It doesn't open.

Howdy Hestersfree,

This can be done through the App Store on the device that you'd like the app installed on.

Apps on iOS

1. Open the App Store on your device.
2. Make sure you are signed in with the same Apple ID used for the original purchase.
3. Tap Updates from the bottom navigation bar. 
   
4. Tap Purchased on the resulting screen.
   
5. Locate the app in your Purchased tab.
6. Tap the download button.
   
7. The app will begin downloading and you'll be taken back to your home screen. 

Downloading past purchases from the App Store, iBookstore, and iTunes Store

http://support.apple.com/kb/HT2519

Cheers,

Allen