Open Terminal in OSX
Enter the command: cd music/itunes/"mobile applications"
Enter the command: ls
You should see Doom.ipa listed. If not then you need to make sure that Doom is backed up to your iTunes Library
Enter the command: cp Doom.ipa Doom.zip
This copies and renames your iTunes backup of Doom
Open Finder
Go to the folder: /Users/username/Music/iTunes/Mobile Applications/ (where "username" is your username)
You should see Doom.zip listed
Double click Doom.zip to uncompress
Navigate to the new folder (should be named "Payload")
Right click on Doom.app and choose "Show Package Contents"
This will open a new Finder displaying the contents of Doom.app
Copy the base folder
Paste the base folder in the DoomSource folder
Open the Doom xcode project located at ../DoomSource/code/iphone/Doom.xcodeproj
Click on "Build and Go" or press "command + R" to build and then run Doom